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| = Fall 2016 = | | = Spring 2018 = |
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| <b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. | | <b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted. |
| | <b>We usually end for questions at 3:15 PM.</b> |
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| If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu. | | If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu. |
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| | <!-- == Thursday, January 25, 2017, TBA== --> |
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| == Thursday, September 8, Daniele Cappelletti, [http://www.math.wisc.edu UW-Madison] == | | == Thursday, February 1, 2017, [https://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [https://math.osu.edu/ OSU]== |
| Title: '''Reaction networks: comparison between deterministic and stochastic models'''
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| Abstract: Mathematical models for chemical reaction networks are widely used in biochemistry, as well as in other fields. The original aim of the models is to predict the dynamics of a collection of reactants that undergo chemical transformations. There exist two standard modeling regimes: a deterministic and a stochastic one. These regimes are chosen case by case in accordance to what is believed to be more appropriate. It is natural to wonder whether the dynamics of the two different models are linked, and whether properties of one model can shed light on the behavior of the other one. Some connections between the two modelling regimes have been known for forty years, and new ones have been pointed out recently. However, many open questions remain, and the issue is still largely unexplored.
| | Title: TBA |
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| == <span style="color:red"> Friday</span>, September 16, <span style="color:red"> 11 am </span> [http://www.baruch.cuny.edu/math/elenak/ Elena Kosygina], [http://www.baruch.cuny.edu/ Baruch College] and the [http://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Mathematics CUNY Graduate Center] ==
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| <div style="width:320px;height:50px;border:5px solid black">
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| <b><span style="color:red"> Please note the unusual day and time </span></b>
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| </div>
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| The talk will be in Van Vleck 910 as usual.
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| Title: '''Homogenization of viscous Hamilton-Jacobi equations: a remark and an application.'''
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| Abstract: It has been pointed out in the seminal work of P.-L. Lions, G. Papanicolaou, and S.R.S. Varadhan that for the first order
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| Hamilton-Jacobi (HJ) equation, homogenization starting with affine initial data should imply homogenization for general uniformly
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| continuous initial data. The argument utilized the properties of the HJ semi-group, in particular, the finite speed of propagation. The
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| last property is lost for viscous HJ equations. We remark that the above mentioned implication holds under natural conditions for both
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| viscous and non-viscous Hamilton-Jacobi equations. As an application of our result, we show homogenization in a stationary ergodic setting for a special class of viscous HJ equations with a non-convex Hamiltonian in one space dimension.
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| This is a joint work with Andrea Davini, Sapienza Università di Roma.
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| == Thursday, September 22, [http://www.math.wisc.edu/~pmwood/ Philip Matchett Wood], [https://www.math.wisc.edu/ UW-Madison] ==
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| Title: Low-degree factors of random polynomials | |
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| Abstract: TBA | | Abstract: TBA |
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| == Thursday, September 29, [http://www.artsci.uc.edu/departments/math/fac_staff.html?eid=najnudjh&thecomp=uceprof Joseph Najnudel], [http://www.artsci.uc.edu/departments/math.html University of Cincinnati]== | | == Thursday, February 8, 2017, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] == |
| Title: TBA
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| == Thursday, October 6, TBA, TBA ==
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| Title: TBA
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| == Thursday, October 13, No Seminar due to [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==
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| For details, see [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium].
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| == Thursday, October 20, [http://www.math.harvard.edu/people/index.html Amol Aggarwal], [http://www.math.harvard.edu/ Harvard] ==
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| Title: TBA
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| == Thursday, October 27, TBA, TBA ==
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| Title: TBA
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| == Thursday, November 3, TBA, TBA ==
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| Title: TBA
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| == Thursday, November 10, TBA, TBA ==
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| Title: TBA
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| == Thursday, November 17, TBA, TBA ==
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| Title: TBA
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| == Thursday, November 24, No Seminar due to Thanksgiving ==
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| == Thursday, December 1, TBA, TBA ==
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| Title: TBA
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| == Thursday, December 8, TBA, TBA ==
| | Title: '''Quantitative CLTs for random walks in random environments''' |
| Title: TBA | |
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| == Thursday, December 15, TBA, TBA ==
| | Abstract:The classical central limit theorem (CLT) states that for sums of a large number of i.i.d. random variables with finite variance, the distribution of the rescaled sum is approximately Gaussian. However, the statement of the central limit theorem doesn't give any quantitative error estimates for this approximation. Under slightly stronger moment assumptions, quantitative bounds for the CLT are given by the Berry-Esseen estimates. In this talk we will consider similar questions for CLTs for random walks in random environments (RWRE). That is, for certain models of RWRE it is known that the position of the random walk has a Gaussian limiting distribution, and we obtain quantitative error estimates on the rate of convergence to the Gaussian distribution for such RWRE. This talk is based on joint works with Sungwon Ahn and Xiaoqin Guo. |
| Title: TBA
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| | == Thursday, February 15, 2017, TBA== |
| | == Thursday, February 22, 2017, [http://pages.cs.wisc.edu/~raskutti/ Garvesh Raskutti] [https://www.stat.wisc.edu/ UW-Madison Stats] and [https://wid.wisc.edu/people/garvesh-raskutti/ WID]== |
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| | Title: TBA |
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| | == Thursday, March 1, 2017, TBA== |
| | == Thursday, March 8, 2017, TBA== |
| | == Thursday, March 15, 2017, TBA== |
| | == Thursday, March 22, 2017, TBA== |
| | == Thursday, March 29, 2017, Spring Break == |
| | == Thursday, April 5, 2017, TBA== |
| | == Thursday, April 12, 2017, TBA== |
| | == Thursday, April 19, 2017, TBA== |
| | == Thursday, April 26, 2017, TBA== |
| | == Thursday, May 3, 2017, TBA== |
| | == Thursday, May 10, 2017, TBA== |
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| == Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] ==
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| Title: '''The quantum integrable particle system on the line'''
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| I will discuss the higher spin six vertex model - an interacting particle
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| system on the discrete 1d line in the Kardar--Parisi--Zhang universality
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| class. Observables of this system admit explicit contour integral expressions
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| which degenerate to many known formulas of such type for other integrable
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| systems on the line in the KPZ class, including stochastic six vertex model,
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| ASEP, various <math>q</math>-TASEPs, and associated zero range processes. The structure
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| of the higher spin six vertex model (leading to contour integral formulas for
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| observables) is based on Cauchy summation identities for certain symmetric
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| rational functions, which in turn can be traced back to the sl2 Yang--Baxter
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| equation. This framework allows to also include space and spin inhomogeneities
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| into the picture, which leads to new particle systems with unusual phase
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| transitions.
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| == Thursday, February 4, [http://homepages.math.uic.edu/~nenciu/Site/Contact.html Inina Nenciu], [http://www.math.uic.edu/ UIC], Joint Probability and Analysis Seminar ==
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| Title: '''On some concrete criteria for quantum and stochastic confinement'''
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| Abstract: In this talk we will present several recent results on criteria ensuring the confinement of a quantum or a stochastic particle to a bounded domain in <math>\mathbb{R}^n</math>. These criteria are given in terms of explicit growth and/or decay rates for the diffusion matrix and the drift potential close to the boundary of the domain. As an application of the general method, we will discuss several cases, including some where the background Riemannian manifold (induced by the diffusion matrix) is geodesically incomplete. These results are part of an ongoing joint project with G. Nenciu (IMAR, Bucharest, Romania).
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| == <span style="color:green">Friday, February 5</span>, [http://www.math.ku.dk/~d.cappelletti/index.html Daniele Cappelletti], [http://www.math.ku.dk/ Copenhagen University], speaks in the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied Math Seminar], <span style="color:green">2:25pm in Room 901 </span>==
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| '''Note:''' Daniele Cappelletti is speaking in the [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS Applied Math Seminar], but his research on stochastic reaction networks uses probability theory and is related to work of our own [http://www.math.wisc.edu/~anderson/ David Anderson].
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| Title: '''Deterministic and Stochastic Reaction Networks'''
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| Abstract: Mathematical models of biochemical reaction networks are of great interest for the analysis of experimental data and theoretical biochemistry. Moreover, such models can be applied in a broader framework than that provided by biology. The classical deterministic model of a reaction network is a system of ordinary differential equations, and the standard stochastic model is a continuous-time Markov chain. A relationship between the dynamics of the two models can be found for compact time intervals, while the asymptotic behaviours of the two models may differ greatly. I will give an overview of these problems and show some recent development.
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| == Thursday, February 25, [http://www.princeton.edu/~rvan/ Ramon van Handel], [http://orfe.princeton.edu/ ORFE] and [http://www.pacm.princeton.edu/ PACM, Princeton] ==
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| Title: '''The norm of structured random matrices'''
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| Abstract: Understanding the spectral norm of random matrices is a problem
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| of basic interest in several areas of pure and applied mathematics. While
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| the spectral norm of classical random matrix models is well understood,
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| existing methods almost always fail to be sharp in the presence of
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| nontrivial structure. In this talk, I will discuss new bounds on the norm
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| of random matrices with independent entries that are sharp under mild
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| conditions. These bounds shed significant light on the nature of the
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| problem, and make it possible to easily address otherwise nontrivial
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| phenomena such as the phase transition of the spectral edge of random band
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| matrices. I will also discuss some conjectures whose resolution would
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| complete our understanding of the underlying probabilistic mechanisms.
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| == Thursday, March 3, [http://www.math.wisc.edu/~janjigia/ Chris Janjigian], [http://www.math.wisc.edu/ UW-Madison] ==
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| Title: '''Large deviations for certain inhomogeneous corner growth models'''
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| Abstract:
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| The corner growth model is a classical model of growth in the plane and is connected to other familiar models such as directed last passage percolation and the TASEP through various geometric maps. In the case that the waiting times are i.i.d. with exponential or geometric marginals, the model is well understood: the shape function can be computed exactly, the fluctuations around the shape function are known to be given by the Tracy-Widom GUE distribution, and large deviation principles corresponding to this limit have been derived.
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| This talk considers the large deviation properties of a generalization of the classical model in which the rates of the exponential are drawn randomly in an appropriate way. We will discuss some exact computations of rate functions in the quenched and annealed versions of the model, along with some interesting properties of large deviations in this model. (Based on joint work with Elnur Emrah.)
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| == Thursday, March 10, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison] ==
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| Title: '''Delocalization and Universality of band matrices.'''
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| Abstract: in this talk we introduce our new work on band matrices, whose eigenvectors and eigenvalues are widely believed to have the same asymptotic behaviors as those of Wigner matrices.
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| We proved that this conjecture is true as long as the bandwidth is wide enough.
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| == Thursday, March 17, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison] ==
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| Title: '''Recovering the Treelike Trend of Evolution Despite Extensive Lateral Genetic Transfer'''
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| Abstract
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| Reconstructing the tree of life from molecular sequences is a fundamental problem in computational
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| biology. Modern data sets often contain large numbers of genes. That can complicate the reconstruction because different genes often undergo different evolutionary histories. This is the case in particular in the presence of lateral genetic transfer (LGT), where a gene is inherited from a distant species rather than an immediate ancestor. Such an event produces a gene tree which is distinct from (but related to) the species phylogeny. In this talk I will sketch recent results showing that, under a natural stochastic model of LGT, the species phylogeny can be reconstructed from gene trees despite surprisingly high rates of LGT.
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| == Thursday, March 24, No Seminar, Spring Break ==
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| == Thursday, March 31, [http://www.ssc.wisc.edu/~whs/ Bill Sandholm], [http://www.econ.wisc.edu/ Economics, UW-Madison] ==
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| Title: '''A Sample Path Large Deviation Principle for a Class of Population Processes'''
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| Abstract: We establish a sample path large deviation principle for sequences of Markov chains arising in game theory and other applications. As the state spaces of these Markov chains are discrete grids in the simplex, our analysis must account for the fact that the processes run on a set with a boundary. A key step in the analysis establishes joint continuity properties of the state-dependent Cramer transform L(·,·), the running cost appearing in the large deviation principle rate function.
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| [http://www.ssc.wisc.edu/~whs/research/ldp.pdf paper preprint]
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| == Thursday, April 7, No Seminar ==
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| == Thursday, April 14, [https://www.math.wisc.edu/~jessica/ Jessica Lin], [https://www.math.wisc.edu/~jessica/ UW-Madison], Joint with [https://www.math.wisc.edu/wiki/index.php/PDE_Geometric_Analysis_seminar PDE Geometric Analysis seminar] ==
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| Title: '''Optimal Quantitative Error Estimates in Stochastic Homogenization for Elliptic Equations in Nondivergence Form'''
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| Abstract: I will present optimal quantitative error estimates in the
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| stochastic homogenization for uniformly elliptic equations in
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| nondivergence form. From the point of view of probability theory,
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| stochastic homogenization is equivalent to identifying a quenched
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| invariance principle for random walks in a balanced random
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| environment. Under strong independence assumptions on the environment,
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| the main argument relies on establishing an exponential version of the
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| Efron-Stein inequality. As an artifact of the optimal error estimates,
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| we obtain a regularity theory down to microscopic scale, which implies
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| estimates on the local integrability of the invariant measure
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| associated to the process. This talk is based on joint work with Scott
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| Armstrong.
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| == Thursday, April 21, [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade], [https://www.cims.nyu.edu/ Courant Institute, NYU] ==
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| Title: '''Freezing and extremes of random unitary matrices'''
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| Abstract: A conjecture of Fyodorov, Hiary & Keating states that the maxima of the characteristic polynomial of random unitary matrices behave like the maxima of a specific class of Gaussian fields, the log-correlated Gaussian fields. We will outline the proof of the conjecture for the leading order of the maximum, and a freezing of the free energy related to the matrix model. This talk is based on a joint work with Louis-Pierre Arguin and David Belius.
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| == Thursday, April 28, [http://www.ime.unicamp.br/~nancy/ Nancy Garcia], [http://www.ime.unicamp.br/conteudo/departamento-estatistica Statistics], [http://www.ime.unicamp.br/ IMECC], [http://www.unicamp.br/unicamp/ UNICAMP, Brazil] ==
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| Title: '''Rumor processes on <math>\mathbb{N}</math> and discrete renewal processe'''
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| Abstract: We study two rumor processes on the positive integers, the dynamics of which are related to an SI epidemic model with long range transmission. Start with one spreader at site <math>0</math> and ignorants situated at some other sites of <math>\mathbb{N}</math>. The spreaders transmit the information within a random distance on their right. Depending on the initial distribution of the ignorants, we obtain probability of survival, information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders. The key step of our approach is to relate this model to the house-of-cards.
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| == Thursday, May 5, [http://math.arizona.edu/~dianeholcomb/ Diane Holcomb], [http://math.arizona.edu/ University of Arizona] ==
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| Title: '''Local limits of Dyson's Brownian Motion at multiple times'''
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| Abstract: Dyson's Brownian Motion may be thought of as a generalization of Brownian Motion to the matrix setting. We can study the eigenvalues of a Dyson's Brownian motion at multiple times. The resulting object has different "color" points corresponding to the eigenvalues at different times. Similar to a single time, the correlation functions of the process may be described in terms of determinantal formulas. We study the local behavior of the eigenvalues as we take the dimension of the associated matrix to infinity. The resulting limiting process in the bulk is again determinantal and is described with an "extended sine kernel." This work aims to give an alternate description of the limiting process in terms of the counting function. In this seminar I will go over the the description and methods for finding such a limit. This is work in progress and is joint with Elliot Paquette (Weizmann Institute).
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| == == | | == == |
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| [[Past Seminars]] | | [[Past Seminars]] |