Difference between revisions of "Past Probability Seminars Spring 2020"
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= Spring 2019 =
<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>
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
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 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
'''Quasi-linear parabolic equations with singular forcing'''
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''
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: We establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson tree is strictly positive if and only if its offspring distribution has an exponential tail, settling a conjecture by Huang and Durrett. On the random graph with degree distribution $D$, we show that if $D$ has an exponential tail, then for small enough $\lambda$ the contact process with the all-infected initial condition survives for polynomial time with high probability, while for large enough $\lambda$ it runs over exponential time with high probability. When $D$ is subexponential, the contact process typically displays long survival for any fixed $\lambda>0$.
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.
Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.
== February 6, [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://lc-tsai.github.io/ Columbia University] ==
== 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: '''When particle systems meet PDEs'''
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: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
'''Langevin Monte Carlo Without Smoothness'''
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==
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.
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
'''A replacement principle for perturbations of non-normal matrices'''
Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.
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 14, TBA ==
== February 27, 2020, No seminar ==
''' '''
== <span style="color:red"> Wednesday, February 27 at 1:10pm</span> [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
''' Large Deviation Principles via Spherical Integrals'''
<div style="width:520px;height:50px;border:5px solid black">
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
<b><span style="color:red">&emsp; Please note the unusual day and time.
&emsp; </span></b>
== March 7, TBA ==
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 $U$;
== March 14, TBA ==
== March 21, Spring Break, 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;
== April 4, TBA ==
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Proccia], [http://www.math.tamu.edu/index.html Texas A&M] ==
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==
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;
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
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.
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
This is a joint work with Belinschi and Guionnet.
== April 26, TBA ==
== March 12, 2020, No seminar ==
== May 2, TBA ==
== March 19, 2020, Spring break ==
== March 26, 2020, CANCELLED, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
== April 2, 2020, CANCELLED, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==
Title: '''The distribution of sandpile groups of random regular graphs'''
== 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) ==
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\operatorname{Aut}(P)|^{-1}</math>. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.
== April 22-24, 2020, CANCELLED, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==
3-day event in Van Vleck 911
== April 23, 2020, CANCELLED, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
== April 30, 2020, CANCELLED, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
Our results extends a recent theorem of Huang saying that the adjacency matrices of random <math>d</math>-regular directed graphs are invertible with high probability to the undirected case.
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
Title: '''Stochastic quantization of Yang-Mills'''
"Stochastic quantization" refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.
In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].
== ==
[[Past Seminars]]
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
January 30, 2020, Scott Smith (UW Madison)
Quasi-linear parabolic equations with singular forcing
February 6, 2020, Cheuk-Yin Lee (Michigan State)
Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points
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
February 27, 2020, No seminar
March 5, 2020, Jiaoyang Huang (IAS)
Large Deviation Principles via Spherical Integrals
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
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)
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