Difference between revisions of "Probability Seminar"

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(April 16, 2020, Jian Ding (University of Pennsilvania))
 
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__NOTOC__
 
__NOTOC__
  
= Spring 2015 =
+
= 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]
  
<!-- [[File:probsem.jpg]] -->
 
</b>
 
 
= =
 
 
== Thursday, January 15, [http://www.stat.berkeley.edu/~racz/ Miklos Racz], [http://statistics.berkeley.edu/ UC-Berkeley Stats] ==
 
 
 
Title: Testing for high-dimensional geometry in random graphs
 
 
Abstract: I will talk about a random geometric graph model, where connections between vertices depend on distances between latent d-dimensional labels; we are particularly interested in the high-dimensional case when d is large. Upon observing a graph, we want to tell if it was generated from this geometric model, or from an Erdos-Renyi random graph. We show that there exists a computationally efficient procedure to do this which is almost optimal (in an information-theoretic sense). The key insight is based on a new statistic which we call "signed triangles". To prove optimality we use a bound on the total variation distance between Wishart matrices and the Gaussian Orthogonal Ensemble. This is joint work with Sebastien Bubeck, Jian Ding, and Ronen Eldan.
 
 
== Thursday, January 22, No Seminar  ==
 
 
== Thursday, January 29, [http://www.math.umn.edu/~arnab/ Arnab Sen], [http://www.math.umn.edu/ University of Minnesota]  ==
 
 
Title: '''Double Roots of Random Littlewood Polynomials'''
 
 
Abstract:
 
We consider random polynomials whose coefficients are independent and uniform on {-1,1}. We will show that the probability that such a polynomial of degree n has a double root is o(n^{-2}) when n+1 is not divisible by 4 and is of the order n^{-2} otherwise. We will also discuss extensions to random polynomials with more general coefficient distributions. 
 
 
This is joint work with Ron Peled and Ofer Zeitouni.
 
 
== Thursday, February 5, No seminar this week  ==
 
 
== Thursday, February 12, No Seminar this week==
 
 
 
<!--
 
== Wednesday, <span style="color:red">February 11</span>, [http://www.math.wisc.edu/~stechmann/ Sam Stechmann], [http://www.math.wisc.edu/ UW-Madison]  ==
 
 
<span style="color:red">Please note the unusual time and room.
 
</span>
 
 
 
Title: Stochastic Models for Rainfall: Extreme Events and Critical Phenomena
 
 
 
Abstract:
 
In recent years, tropical rainfall statistics have been shown to conform to paradigms of critical phenomena and statistical physics. In this talk, stochastic models will be presented as prototypes for understanding the atmospheric dynamics that leads to these statistics and extreme events. Key nonlinear ingredients in the models include either stochastic jump processes or thresholds (Heaviside functions). First, both exact solutions and simple numerics are used to verify that a suite of observed rainfall statistics is reproduced by the models, including power-law distributions and long-range correlations. Second, we prove that a stochastic trigger, which is a time-evolving indicator of whether it is raining or not, will converge to a deterministic threshold in an appropriate limit. Finally, we discuss the connections among these rainfall models, stochastic PDEs, and traditional models for critical phenomena.
 
--->
 
 
== Thursday, February 19, [http://www.math.purdue.edu/people/bio/guo297 Xiaoqin Guo], [http://www.math.purdue.edu/ Purdue]  ==
 
 
Title: Quenched invariance principle for random walks in time-dependent random environment
 
 
Abstract: In this talk we discuss random walks in a time-dependent zero-drift random environment in <math>Z^d</math>. We prove a quenched invariance principle under an appropriate moment condition. The proof is based on the use of a maximum principle for parabolic difference operators. This is a joint work with Jean-Dominique Deuschel and Alejandro Ramirez.
 
 
== Thursday, February 26, [http://wwwf.imperial.ac.uk/~dcrisan/ Dan Crisan], [http://www.imperial.ac.uk/natural-sciences/departments/mathematics/ Imperial College London]  ==
 
 
Title: '''Smoothness properties of randomly perturbed semigroups with application to nonlinear filtering'''
 
 
Abstract:
 
In this talk I will discuss sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. The estimates we derive have sharp small time asymptotics
 
 
   
 
   
This is joint work with Terry Lyons (Oxford) and Christian Literrer (Ecole Polytechnique) and is based on the paper
+
== 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
D Crisan, C Litterer, T Lyons, Kusuoka–Stroock gradient bounds for the solution of the filtering equation, Journal of Functional Analysis, 2105
+
'''
 
 
== Wednesday, <span style="color:red">March 11</span>, [http://www.math.wisc.edu/~stechmann/ Sam Stechmann], [http://www.math.wisc.edu/ UW-Madison], <span style="color:red">2:25pm Van Vleck B321</span>  ==
 
 
 
<span style="color:red">Please note the unusual time and room.
 
</span>
 
 
 
 
 
Title: Stochastic Models for Rainfall: Extreme Events and Critical Phenomena
 
 
 
 
 
Abstract:
 
In recent years, tropical rainfall statistics have been shown to conform to paradigms of critical phenomena and statistical physics. In this talk, stochastic models will be presented as prototypes for understanding the atmospheric dynamics that leads to these statistics and extreme events. Key nonlinear ingredients in the models include either stochastic jump processes or thresholds (Heaviside functions). First, both exact solutions and simple numerics are used to verify that a suite of observed rainfall statistics is reproduced by the models, including power-law distributions and long-range correlations. Second, we prove that a stochastic trigger, which is a time-evolving indicator of whether it is raining or not, will converge to a deterministic threshold in an appropriate limit. Finally, we discuss the connections among these rainfall models, stochastic PDEs, and traditional models for critical phenomena.
 
 
 
 
 
<!--
 
== Thursday, March 12, TBA  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
-->
 
 
 
== Thursday, March 19,  [http://www.cmc.edu/pages/faculty/MHuber/ Mark Huber], [http://www.cmc.edu/math/ Claremont McKenna Math]  ==
 
 
 
Title: Understanding relative error in Monte Carlo simulations
 
 
 
Abstract:  The problem of estimating the probability <math>p</math> of heads on an unfair coin has been around for centuries, and has inspired numerous advances in probability such as the Strong Law of Large Numbers and the Central Limit Theorem.  In this talk, I'll consider a new twist:  given an estimate <math>\hat p</math>, suppose we want to understand the behavior of the relative error <math>(\hat p - p)/p</math>.  In classic estimators, the values that the relative error can take on depends on the value of <math>p</math>.  I will present a new estimate with the remarkable property that the distribution of the relative error does not depend in any way on the value of <math>p</math>.  Moreover, this new estimate is very fast:  it takes a number of coin flips that is very close to the theoretical minimum.  Time permitting, I will also discuss new ways to use concentration results for estimating the mean of random variables where normal approximations do not apply.
 
 
 
== Thursday, March 26, [http://mathsci.kaist.ac.kr/~jioon/ Ji Oon Lee], [http://www.kaist.edu/html/en/index.html KAIST]  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
 
 
== Thursday, April 2, No Seminar, Spring Break  ==
 
 
 
 
 
 
 
 
 
== Thursday, April 9, [http://www.math.wisc.edu/~emrah/ Elnur Emrah], [http://www.math.wisc.edu/ UW-Madison]  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
 
 
== Thursday, April 16, TBA  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
== Thursday, April 23, [http://people.math.osu.edu/nguyen.1261/ Hoi Nguyen], [http://math.osu.edu/ Ohio State University]  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
== Thursday, April 30, TBA  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
 
 
== Thursday, May 7, TBA  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
 
 
 
 
 
 
 
 
 
 
 
 
<!--
 
== Thursday, December 11, TBA  ==
 
 
 
Title: TBA
 
 
 
Abstract:
 
-->
 
 
 
 
 
 
 
<!--
 
 
 
== Thursday, September 11, <span style="color:red">Van Vleck B105,</span> [http://www.math.wisc.edu/~mmwood/ Melanie Matchett Wood], UW-Madison ==
 
 
 
Please note the non-standard room.
 
 
 
Title: '''The distribution of sandpile groups of random graphs'''
 
 
 
Abstract:<br>
 
The sandpile group is an abelian group associated to a graph, given as
 
the cokernel of the graph Laplacian.  An Erdős–Rényi random graph
 
then gives some distribution of random abelian groups.  We will give
 
an introduction to various models of random finite abelian groups
 
arising in number theory and the connections to the distribution
 
conjectured by Payne et. al. for sandpile groups.  We will talk about
 
the moments of random finite abelian groups, and how in practice these
 
are often more accessible than the distributions themselves, but
 
frustratingly are not a priori guaranteed to determine the
 
distribution.  In this case however, we have found the moments of the
 
sandpile groups of random graphs, and proved they determine the
 
measure, and have proven Payne's conjecture.
 
 
 
== Thursday, September 18, [http://www.math.purdue.edu/~peterson/ Jonathon Peterson], [http://www.math.purdue.edu/ Purdue University]  ==
 
 
 
Title: '''Hydrodynamic limits for directed traps and systems of independent RWRE'''
 
 
 
Abstract:
 
 
 
We study the evolution of a system of independent random walks in a common random environment (RWRE). Previously a hydrodynamic limit was proved in the case where the environment is such that the random walks are ballistic (i.e., transient with non-zero speed <math>v_0 \neq 0)</math>. In this case it was shown that the asymptotic particle density is simply translated deterministically by the speed $v_0$. In this talk we will consider the more difficult case of RWRE that are transient but with $v_0=0$. Under the appropriate space-time scaling, we prove a hydrodynamic limit for the system of random walks. The statement of the hydrodynamic limit that we prove is non-standard in that the evolution of the asymptotic particle density is given by the solution of a random rather than a deterministic PDE. The randomness in the PDE comes from the fact that under the hydrodynamic scaling the effect of the environment does not ``average out'' and so the specific instance of the environment chosen actually matters.
 
 
 
The proof of the hydrodynamic limit for the system of RWRE will be accomplished by coupling the system of RWRE with a simpler model of a system of particles in an environment of ``directed traps.'' This talk is based on joint work with Milton Jara.
 
 
 
== Thursday, September 25, [http://math.colorado.edu/~seor3821/ Sean O'Rourke],  [http://www.colorado.edu/math/ University of Colorado Boulder]  ==
 
 
 
Title: '''Singular values and vectors under random perturbation'''
 
 
 
Abstract:
 
Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. A natural question is the following. How much does a small perturbation to the matrix change the singular values and vectors?
 
 
 
Classical (deterministic) theorems, such as those by Davis-Kahan, Wedin, and Weyl, give tight estimates for the worst-case scenario. In this talk, I will consider the case when the perturbation is random. In this setting, better estimates can be achieved when our matrix has low rank.  This talk is based on joint work with Van Vu and Ke Wang.
 
 
 
== Thursday, October 2, [http://www.math.wisc.edu/~jyin/jun-yin.html Jun Yin], [http://www.math.wisc.edu/ UW-Madison]  ==
 
 
 
Title: '''Anisotropic local laws for random matrices'''
 
 
 
Abstract:
 
In this talk, we introduce a new method of deriving  local laws of random matrices.  As applications, we will show the local laws  and some universality results on general sample covariance matrices: TXX^*T^* (where $T$ is non-square deterministic matrix),  and deformed Wigner matrix: H+A (where A is deterministic symmetric matrix). Note: here $TT^*$ and $A$ could be full rank matrices.
 
 
 
== Thursday, October 9, No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium]  ==
 
 
 
No seminar due to [http://www.math.northwestern.edu/mwp/ Midwest Probability Colloquium].
 
 
 
 
 
== Thursday, October 16, [http://www.math.utah.edu/~firas/ Firas Rassoul-Agha], [http://www.math.utah.edu/ University of Utah]==
 
 
 
Title: '''The growth model: Busemann functions, shape, geodesics, and other stories'''
 
 
 
Abstract:
 
We consider the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles define solutions to variational formulas that characterize limit shapes and yield new results for Busemann functions, geodesics and the competition interface.  This is joint work with Nicos Georgiou and Timo Seppalainen.
 
 
 
 
 
== Thursday, November 6, Vadim Gorin, [http://www-math.mit.edu/people/profile.php?pid=1415 MIT]  ==
 
  
Title: '''Multilevel Dyson Brownian Motion and its edge limits.'''
+
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).
  
Abstract: The GUE Tracy-Widom distribution is known to govern the large-time asymptotics for a variety of
+
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
interacting particle systems on one side, and the asymptotic behavior for largest eigenvalues of
+
''' '''
random Hermitian matrices on the other side. In my talk I will explain some reasons for this
 
connection between two seemingly unrelated classes of stochastic systems, and how this relation can
 
be extended to general beta random matrices. A multilevel extension of the Dyson Brownian Motion
 
will be the central object in the discussion.
 
  
(Based on joint papers with Misha Shkolnikov.)
+
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==
 +
''' '''
  
==<span style="color:red"> Friday</span>, November 7, [http://tchumley.public.iastate.edu/ Tim Chumley], [http://www.math.iastate.edu/ Iowa State University] ==
+
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
 +
''' '''
  
<span style="color:darkgreen">Please note the unusual day.</span>
+
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
 +
''' '''
  
Title: '''Random billiards and diffusion'''
+
== February 27, 2020, TBA ==
 +
''' '''
  
Abstract: We introduce a class of random dynamical systems derived from billiard maps and study a certain Markov chain derived from them. We then discuss the interplay between the billiard geometry and stochastic properties of the random system.  The main results presented investigate the affect of billiard geometry on a diffusion process obtained from an appropriate scaling limit of the Markov chain.
+
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
 +
''' '''
  
== Thursday, November 13, [http://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], [http://www.math.wisc.edu/ UW-Madison]==
+
== March 12, 2020, TBA ==
 +
''' '''
  
Title: '''Variational formulas for directed polymer and percolation models'''
+
== March 26, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
 +
''' '''
  
Abstract:
+
== April 2, 2020, TBA ==
Explicit formulas for subadditive limits of polymer and percolation models in probability and statistical mechanics have been difficult to find. We describe variational formulas for these limits and their connections with other features of the models such as Busemann functions and Kardar-Parisi-Zhang (KPZ) fluctuation exponents.
+
''' '''
  
 +
== April 9, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==
 +
''' '''
  
 +
== April 16, 2020, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==
 +
''' '''
  
== <span style="color:red">Monday</span>, December 1, [http://www.ma.utexas.edu/users/jneeman/index.html Joe Neeman], [http://www.ma.utexas.edu/ UT-Austin], <span style="color:red">4pm, Room B239 Van Vleck Hall</span>==
+
== April 22-24, 2020, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==
  
<span style="color:darkgreen">Please note the unusual time and room.</span>
+
3-day event in Van Vleck 911
  
Title: '''Some phase transitions in the stochastic block model'''
+
== April 23, 2020, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==
  
Abstract: The stochastic block model is a random graph model that was originally 30 years ago to study community detection in networks. To generate a random graph from this model, begin with two classes of vertices and then connect each pair of vertices independently at random, with probability p if they are in the same class and probability q otherwise. Some questions come to mind: can we reconstruct the classes if we only observe the graph? What if we only want to partially reconstruct the classes? How different is this model from an Erdos-Renyi graph anyway? The answers to these questions depend on p and q, and we will say exactly how.
+
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
  
== Thursday, December 4, Arjun Krishnan, [http://www.fields.utoronto.ca/ Fields Institute] ==
+
== April 30, 2020, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
 +
''' '''
  
Title: '''Variational formula for the time-constant of first-passage percolation'''
 
  
Abstract:
 
Consider first-passage percolation with positive, stationary-ergodic
 
weights on the square lattice in d-dimensions. Let <math>T(x)</math> be the
 
first-passage time from the origin to <math>x</math> in <math>Z^d</math>. The convergence of
 
<math>T([nx])/n</math> to the time constant as <math>n</math> tends to infinity is a consequence
 
of the subadditive ergodic theorem. This convergence can be viewed as
 
a problem of homogenization for a discrete Hamilton-Jacobi-Bellman
 
(HJB) equation. By borrowing several tools from the continuum theory
 
of stochastic homogenization for HJB equations, we derive an exact
 
variational formula (duality principle) for the time-constant. Under a
 
symmetry assumption, we will use the variational formula to construct
 
an explicit iteration that produces the limit shape.
 
  
  
-->
 
  
== ==
 
  
  
  
 
[[Past Seminars]]
 
[[Past Seminars]]

Latest revision as of 07:12, 20 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)

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

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, TBA

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