Difference between revisions of "Probability Seminar"

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(Thursday, April 14, Jessica Lin, UW-Madison, Joint with PDE Geometric Analysis seminar)
(February 6, 2020, Cheuk-Yin Lee (Michigan State))
 
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__NOTOC__
 
__NOTOC__
  
= Spring 2016 =
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= Spring 2020 =
  
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
+
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
 +
<b>We  usually end for questions at 3:20 PM.</b>
  
<b>
+
If you would like to sign up for the email list to receive seminar announcements then please send an email to  
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.
+
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
</b>
 
  
 +
 +
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==
 +
'''Non-existence of bi-infinite geodesics in the exponential corner growth model
 +
'''
  
 +
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s.  A non-existence proof  in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in  November 2018. Their proof utilizes estimates from integrable probability.    This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).
  
== Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] ==
+
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
 +
'''Quasi-linear parabolic equations with singular forcing'''
  
Title: '''The quantum integrable particle system on the line'''
+
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral.  By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise.  In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise.  The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.
  
I will discuss the higher spin six vertex model - an interacting  particle
+
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution.  These are known as quasi-linear equationsOur main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization.  Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.
system on the discrete 1d line in the Kardar--Parisi--Zhang universality
 
class. Observables of this system admit explicit contour integral expressions
 
which degenerate to many known formulas of such type for other integrable
 
systems on the line in the KPZ class, including stochastic six vertex model,
 
ASEP, various <math>q</math>-TASEPs, and associated zero range processes. The structure
 
of the higher spin six vertex model (leading to contour integral formulas for
 
observables) is based on Cauchy summation identities for certain symmetric
 
rational functions, which in turn can be traced back to the sl2 Yang--Baxter
 
equation. This framework allows to also include space and spin inhomogeneities
 
into the picture, which leads to new particle systems with unusual phase
 
transitions.
 
  
== 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 ==
+
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==
 +
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''
  
Title: '''On some concrete criteria for quantum and stochastic confinement'''
+
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.
  
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).
+
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
 +
''' '''
  
== <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>==
+
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
 +
''' '''
  
'''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].
+
== February 27, 2020, TBA ==
 +
''' '''
  
Title: '''Deterministic and Stochastic Reaction Networks'''
+
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
 +
''' '''
  
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.
+
== March 12, 2020, TBA ==
 +
''' '''
  
<!--== Thursday, February 11, TBA ==-->
+
== March 26, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
<!--== Thursday, February 18, TBA ==-->
+
''' '''
  
== Thursday, February 25, [http://www.princeton.edu/~rvan/ Ramon van Handel], [http://orfe.princeton.edu/ ORFE] and [http://www.pacm.princeton.edu/ PACM, Princeton] ==
+
== April 2, 2020, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==
 +
''' '''
  
Title: '''The norm of structured random matrices'''
+
== April 9, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==
 +
''' '''
  
Abstract: Understanding the spectral norm of random matrices is a problem
+
== April 16, 2020, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==
of basic interest in several areas of pure and applied mathematics. While
+
''' '''
the spectral norm of classical random matrix models is well understood,
 
existing methods almost always fail to be sharp in the presence of
 
nontrivial structure. In this talk, I will discuss new bounds on the norm
 
of random matrices with independent entries that are sharp under mild
 
conditions. These bounds shed significant light on the nature of the
 
problem, and make it possible to easily address otherwise nontrivial
 
phenomena such as the phase transition of the spectral edge of random band
 
matrices. I will also discuss some conjectures whose resolution would
 
complete our understanding of the underlying probabilistic mechanisms.
 
  
== Thursday, March 3, [http://www.math.wisc.edu/~janjigia/ Chris Janjigian], [http://www.math.wisc.edu/ UW-Madison] ==
+
== April 22-24, 2020, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==
  
Title: '''Large deviations for certain inhomogeneous corner growth models'''
+
3-day event in Van Vleck 911
  
Abstract:
+
== April 23, 2020, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==
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.
 
  
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.)
+
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
  
== Thursday, March 10, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison] ==
+
== April 30, 2020, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
 +
''' '''
  
Title: '''Delocalization and Universality of band matrices.'''
 
  
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.
 
We proved that this conjecture is true as long as the bandwidth is wide enough.
 
  
== Thursday,  March 17, [http://www.math.wisc.edu/~roch/ Sebastien Roch], [http://www.math.wisc.edu/ UW-Madison] ==
 
  
  
Title: '''Recovering the Treelike Trend of Evolution Despite Extensive Lateral Genetic Transfer'''
 
 
Abstract
 
Reconstructing the tree of life from molecular sequences is a fundamental problem in computational
 
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.
 
 
== Thursday,  March 24, No Seminar, Spring Break ==
 
 
== Thursday,  March 31, [http://www.ssc.wisc.edu/~whs/ Bill Sandholm], [http://www.econ.wisc.edu/ Economics, UW-Madison] ==
 
 
Title: '''A Sample Path Large Deviation Principle for a Class of Population Processes'''
 
 
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.
 
 
[http://www.ssc.wisc.edu/~whs/research/ldp.pdf paper preprint]
 
 
== Thursday,  April 7, TBA ==
 
 
== 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] ==
 
 
Title: '''Optimal Quantitative Error Estimates in Stochastic
 
Homogenization for Elliptic Equations in Nondivergence Form'''
 
 
Abstract: I will present optimal quantitative error estimates in the
 
stochastic homogenization for uniformly elliptic equations in
 
nondivergence form. From the point of view of probability theory,
 
stochastic homogenization is equivalent to identifying a quenched
 
invariance principle for random walks in a balanced random
 
environment. Under strong independence assumptions on the environment,
 
the main argument relies on establishing an exponential version of the
 
Efron-Stein inequality. As an artifact of the optimal error estimates,
 
we obtain a regularity theory down to microscopic scale, which implies
 
estimates on the local integrability of the invariant measure
 
associated to the process. This talk is based on joint work with Scott
 
Armstrong.
 
 
== Thursday,  April 21, [http://www.cims.nyu.edu/~bourgade/ Paul Bourgade], [https://www.cims.nyu.edu/ Courant Institute, NYU] ==
 
 
== Thursday,  April 28, Nancy Garcia, [http://www.ime.unicamp.br/conteudo/departamento-estatistica Statistics], [http://www.ime.unicamp.br/ IMECC], [http://www.unicamp.br/unicamp/ UNICAMP, Brazil] ==
 
 
== Thursday,  May 5, TBA ==
 
 
== ==
 
  
  
  
 
[[Past Seminars]]
 
[[Past Seminars]]

Latest revision as of 09:50, 23 January 2020


Spring 2020

Thursdays in 901 Van Vleck Hall at 2:30 PM, unless otherwise noted. We usually end for questions at 3:20 PM.

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


January 23, 2020, Timo Seppalainen (UW Madison)

Non-existence of bi-infinite geodesics in the exponential corner growth model

Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).

January 30, 2020, Scott Smith (UW Madison)

Quasi-linear parabolic equations with singular forcing

The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.

In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.

February 6, 2020, Cheuk-Yin Lee (Michigan State)

Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points

In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.

February 13, 2020, Jelena Diakonikolas (UW Madison)

February 20, 2020, Philip Matchett Wood (UC Berkeley)

February 27, 2020, TBA

March 5, 2020, Jiaoyang Huang (IAS)

March 12, 2020, TBA

March 26, 2020, Philippe Sosoe (Cornell)

April 2, 2020, Tianyu Liu (UW Madison)

April 9, 2020, Alexander Dunlap (Stanford)

April 16, 2020, Jian Ding (University of Pennsylvania)

April 22-24, 2020, FRG Integrable Probability meeting

3-day event in Van Vleck 911

April 23, 2020, Martin Hairer (Imperial College)

Wolfgang Wasow Lecture at 4pm in Van Vleck 911

April 30, 2020, Will Perkins (University of Illinois at Chicago)





Past Seminars