Difference between revisions of "Past Probability Seminars Spring 2020"

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__NOTOC__
 
__NOTOC__
  
== Fall 2012 ==
+
= Spring 2020 =
  
 +
<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>
  
Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. If you would like to receive announcements about upcoming seminars, please visit [https://www-old.cae.wisc.edu/mailman/listinfo/apseminar this page] to sign up for the email list.
+
If you would like to sign up for the email list to receive seminar announcements then please send an email to
 +
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
  
 +
 +
== 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
 +
'''
  
[[Past Seminars]]
+
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, September 13, Sebastien Roch, UW-Madison ==
+
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
 +
'''Quasi-linear parabolic equations with singular forcing'''
  
Title: Markov models on trees: Variants of the reconstruction problem
+
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.
  
Abstract: 
+
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.
I will consider the so-called `reconstruction problem': how accurately
 
can one guess the state at the root of a Markov chain on a finite tree,  
 
given the states at the leaves? I will introduce variants of this problem
 
that arise naturally in connection with applications in molecular
 
evolution, and discuss recent results and open problems. Based
 
on joint works with Andoni, Daskalakis, Hassidim, Mossel and
 
Sly.
 
  
 +
== 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'''
  
 +
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.
  
== Thursday, September 20, Jun Yin, UW-Madison ==
+
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
 +
'''Langevin Monte Carlo Without Smoothness'''
  
Title: Some new results on random matrices.
+
Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation.
 +
Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.
  
Abstract: In this talk, we will introduce some new results on random
+
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
matrices, especially the necessary and sufficient conditions for universality
+
'''A replacement principle for perturbations of non-normal matrices'''
at the edge and a new result on the circular law.
 
  
== <font color="red">Friday</font>, October 5, Nicos Georgiou, University of Utah ==
+
There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added.  However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added.  Much of the work is this situation has focused on iid random gaussian perturbations.  In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure.  Interestingly, this even allows for deterministic perturbations to be considered.  Joint work with Sean O'Rourke.
  
Title: Busemann functions and variational formula for last passage
+
== February 27, 2020, No seminar ==
percolation.
+
''' '''
  
Abstract: Directed last passage percolation on the two dimensional lattice is
+
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
exactly solvable when the weight distribution is i.i.d. exponential or
+
''' Large Deviation Principles via Spherical Integrals'''
geometric. The reason for that is the Burke property associated to a model
 
with "boundaries".
 
  
We investigate the solvable model further in order to generalize the idea
+
In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain
of boundaries into the general setting, and we compute a variational
 
formula for passage times for more general weights. The variatonal formula
 
is given in terms of Busemann functions and all restrictive assumptions on
 
the environment are to guarantee their existence.
 
  
Joint work with T. Seppalainen, F. Rassoul-Agha and A. Yilmaz.
+
1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;
  
== Thursday, October 11, No seminar ==
+
2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;
  
because of the MIDWEST PROBABILITY COLLOQUIUM
+
3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;
  
 +
4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.
  
== Thursday, October 18, Jason Swanson, University of Central Florida ==
+
This is a joint work with Belinschi and Guionnet.
  
Title: Correlations within the signed cubic variation of fractional Brownian motion
+
== March 12, 2020, No seminar ==
 +
''' '''
  
Abstract:  The signed cubic variation of the fractional Brownian motion, <math>B</math>, with Hurst parameter <math>H=1/6</math>, is a concept built upon the fact that the sequence, <math>\{W_n\}</math>, of sums of cubes of increments of <math>B</math> converges in law to an independent Brownian motion as the size of the increments tends to zero. In joint work with Chris Burdzy and David Nualart, we study the convergence in law of two subsequences of  <math>\{W_n\}</math>. We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.
+
== March 19, 2020, Spring break ==
 +
''' '''
  
== Thursday, October 25, Mihai Stoiciu, Williams College ==
+
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
 +
''' '''
  
Title: Random Matrices with Poisson Eigenvalue Statistics
+
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==
 +
''' '''
  
Abstract: Several classes of random self-adjoint and random unitary matrices exhibit Poisson microscopic eigenvalue statistics. We will outline the general strategy for proving these results and discuss other models where the Poisson statistics is conjectured. We will also explain how changes in the distribution of the matrix coefficients produce changes in the microscopic eigenvalue distribution and give a transition from Poisson to the picket fence distribution.
+
== April 9, 2020, CANCELLED, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==
 +
''' '''
  
 +
== April 16, 2020, CANCELLED, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==
 +
''' '''
  
 +
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==
  
 +
3-day event in Van Vleck 911
  
== Thursday, November 8, Michael Kozdron, University of Regina ==
+
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==
  
Title: The Green's function for the radial Schramm-Loewner evolution
+
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
  
Abstract:   The Schramm-Loewner evolution (SLE), a one-parameter family of random two-dimensional growth processes introduced in 1999 by the late Oded Schramm, has proved to be very useful for studying the scaling limits of discrete models from statistical mechanics. One tool for analyzing SLE itself is the Green's function. An exact formula for the Green's function for chordal SLE was used by Rohde and Schramm (2005) and Beffara (2008) for determining the Hausdorff dimension of the SLE trace. In the present talk, we will discuss the Green's function for radial SLE. Unlike the chordal case, an exact formula is known only when the SLE parameter value is 4. For other values, a formula is available in terms of an expectation with respect to SLE conditioned to go through a point. This talk is based on joint work with Tom Alberts and Greg Lawler.
+
== April 30, 2020, CANCELLED, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
 +
''' '''
  
  
  
== Thursday, November 15, Gregorio Moreno Flores, University of Wisconsin - Madison ==
 
  
Title:  Directed polymers and the stochastic heat equation
 
  
Abstract:  We show how some properties of the solutions of the Stochastic Heat Equation (SHE) can be derived from directed polymers in random environment. In particular, we show:
 
* A new proof of the positivity of the solutions of the SHE
 
* Improved bounds on the negative moments of the SHE
 
* Results on the fluctuations of the log of the SHE in equilibrium, namely, the Cole-Hopf solution of the KPZ equation (if time allows).
 
  
  
== <font color="red">Tuesday</font>, November 27, Michael Damron, Princeton ==
 
  
Title: Busemann functions and infinite geodesics in first-passage percolation
+
[[Past Seminars]]
 
 
Abstract: In first-passage percolation we study the chemical
 
distance in the weighted graph Z^d, where the edge weights are given
 
by a translation-ergodic (typically i.i.d.) distribution. A main open
 
question is to describe the behavior of very long or infinite
 
geodesics. In particular, one would like to know if there are infinite
 
geodesics with asymptotic directions, how many are there, and if
 
infinite geodesics in the same direction coalesce. Some of these
 
questions were addressed in the late 90's by Newman and collaborators
 
under strong assumptions on the limiting shape and weight
 
distribution. I will discuss work with Jack Hanson (Ph. D. student at
 
Princeton) where we develop a framework for working with
 
distributional limits of Busemann functions and use them to prove a
 
form of coalescence of geodesics constructed in any deterministic
 
direction. We also prove existence of infinite geodesics which are
 
asymptotically directed in sectors. Last, we introduce a purely
 
directional condition which replaces Newman's global curvature
 
condition and whose assumption implies the existence of directional
 
geodesics.
 
 
 
 
 
 
 
== Thursday, December 6, Scott McKinley, University of Florida ==
 
 
 
Title: Sensing and Decision-Making in Random Search
 
 
 
Abstract:  Many organisms locate resources in environments in which sensory signals are rare, noisy, and lack directional information. Recent studies of search in such environments model search behavior using random walks (e.g., Levy walks) that match empirical move- ment distributions. We extend this modeling approach to include searcher responses to noisy sensory data. The results of numerical simulation show that including even a simple response to noisy sensory data can dominate other features of random search, resulting in lower mean search times and decreased risk of long intervals between target encounters. In particular, we show that a lack of signal is not a lack of information. Searchers that receive no signal can quickly abandon target-poor regions. On the other hand, receiving a strong signal leads a searcher to concentrate search effort near targets. These responses cause simulated searchers to exhibit an emergent area-restricted search behavior similar to that observed of many organisms in nature.
 
 
 
 
 
 
 
 
 
== Thursday, December 13, Karl Liechty, University of Michigan ==
 
 
 
Title: TBA
 
 
 
Abstract:  TBA
 

Latest revision as of 17:18, 12 August 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)

Langevin Monte Carlo Without Smoothness

Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is understood mainly in the setting of smooth (gradient-Lipschitz) log-densities, a serious limitation for applications in machine learning. We remove this limitation by providing polynomial-time convergence guarantees for a variant of LMC in the setting of non-smooth log-concave distributions. At a high level, our results follow by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that we add to the iterates of the algorithm and while controlling the bias and variance that are induced by this perturbation. Based on joint work with Niladri Chatterji, Michael I. Jordan, and Peter L. Bartlett.

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

A replacement principle for perturbations of non-normal matrices

There are certain non-normal matrices whose eigenvalues can change dramatically when a small perturbation is added. However, when that perturbation is an iid random matrix, it appears that the eigenvalues become stable after perturbation and only change slightly when further small perturbations are added. Much of the work is this situation has focused on iid random gaussian perturbations. In this talk, we will discuss work on a universality result that allows for consideration of non-gaussian perturbations, and that shows that all perturbations satisfying certain conditions will produce the same limiting eigenvalue measure. Interestingly, this even allows for deterministic perturbations to be considered. Joint work with Sean O'Rourke.

February 27, 2020, No seminar

March 5, 2020, Jiaoyang Huang (IAS)

Large Deviation Principles via Spherical Integrals

In this talk, I'll explain a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the asymptotics of spherical integrals obtained by Guionnet and Zeitouni. As examples, we obtain

1) the large deviation principle for the empirical distribution of the diagonal entries of $UB_NU^*$, for a sequence of $N\times N$ diagonal matrices $B_N$ and unitary/orthogonal Haar distributed matrices $U$;

2) the large deviation upper bound for the empirical eigenvalue distribution of $A_N+UB_NU^*$, for two sequences of $N\times N$ diagonal matrices $A_N, B_N$, and their complementary lower bounds at "good" probability distributions;

3) the large deviation principle for the Kostka number $K_{\lambda_N \eta_N}$, for two sequences of partitions $\lambda_N, \eta_N$ with at most $N$ rows;

4) the large deviation upper bound for the Littlewood-Richardson coefficients $c_{\lambda_N \eta_N}^{\kappa_N}$, for three sequences of partitions $\lambda_N, \eta_N, \kappa_N$ with at most $N$ rows, and their complementary lower bounds at "good" probability distributions.

This is a joint work with Belinschi and Guionnet.

March 12, 2020, No seminar

March 19, 2020, Spring break

March 26, 2020, CANCELLED, Philippe Sosoe (Cornell)

April 2, 2020, CANCELLED, Tianyu Liu (UW Madison)

April 9, 2020, CANCELLED, Alexander Dunlap (Stanford)

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

April 22-24, 2020, CANCELLED, FRG Integrable Probability meeting

3-day event in Van Vleck 911

April 23, 2020, CANCELLED, Martin Hairer (Imperial College)

Wolfgang Wasow Lecture at 4pm in Van Vleck 911

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





Past Seminars