**The 21st Northeast Probability Seminar** will be held on Thursday and Friday, November 17-18, 2022. The invited speakers are Neil O’Connell, Raluca Balan, Davar Koshnevisan, and Tianyi Zheng.

**Plenary talks
**

**Speaker: **Raluca Balan

**Title: **Recent advances on SPDEs with colored noise in time

**Abstract:** This talk will start with a gentle introduction to the theory of

stochastic partial differential equations (SPDEs) using the random field approach. The goal is to review some recent results about SPDEs driven by a Gaussian noise which is homogeneous in space and colored in time. A basic example is when the noise is generated by a fractional Brownian sheet with different Hurst indices in time and space.

The focus will be on the parabolic Anderson model and the hyperbolic Anderson model. Using basic elements of Malliavin calculus, we can define two type of solutions for these models, depending on how we interpret the stochastic integral used in the definition of the solution: in the Skorohod sense, or in the Stratonovich sense. These solutions have interesting asymptotic properties, which can be developed using more advanced Malliavin calculus techniques. Among these, we will examine the exponential behavior of the moments as time gets large, and the limiting distribution of the spatial integral as the spatial integration region gets large. No prior knowledge of Malliavin calculus is required for this talk.

**Speaker: **Neil O’Connell

**Title: **Some integrable models in probability

**Abstract: **In recent years, the interplay between probability and integrable systems has been very fruitful, most notably in the context of random matrix theory and surface growth models in 1+1 dimensions. In this talk, I will discuss some examples related to the Toda lattice. The latter was introduced by Morikazu Toda in 1967 as a simple model for a one-dimensional chain of particles with non-linear nearest neighbour interaction, and is one of the earliest examples of a non-linear completely integrable system. This talk is aimed at a general probability audience and no prior knowledge of integrable systems will be assumed.

**Speaker: **Davar Koshnevisan

**Title: **Valleys for the stochastic heat equation

**Abstract: **We describe some ongoing work with Kunwoo Kim (POSTECH) and Carl Mueller (Rochester) on the valleys, also known as void regions, in between the tall spatial peaks of a family of stochastic heat equations. The main results are large-time quantitative bounds on the maximum height and maximum length of the valley that straddles a given point in space.

**Speaker: **Tianyi Zheng

**Title: **Furstenberg entropy spectrum of stationary actions

**Abstract: **The study of stationary actions of groups and connections to random walks was initiated by Furstenberg, and later plays a role in the development of rigidity theory. The Furstenberg entropy is a fundamental invariant defined for a stationary system. In this talk we will discuss some aspect of the question: given a group, what is the range of the Furstenberg entropy of ergodic stationary actions of it? For the linear group SL(d,R) and its lattices, the constraints on this spectrum are closely related to structure theorems due to Nevo and Zimmer; and entropy values can be realized through random walks on random stationary graphs.

**Schedule**

**Thursday Nov 17** 9-9:45 Refreshments (508 Math) 9:45-10:00 Registration (412 CEPSR) 10-11 Raluca Balan (412 CEPSR) 11-11:15 Bathroom Break 11:15-12:15 Neil O’Connell (412 CEPSR) 12:15-1:45pm Lunch (Around Campus) 2:00-2:45 Short Talks (412 CEPSR) 2:45-3:00 Bathroom Break 3:00-4:00 Short Talks (412 CEPSR) 4:00-4:45 Tea (508 Math) 4:45-6:00 Short Talks (412 CEPSR) 6:00-7:00 Reception (508 Math)**Friday Nov 18** 9-9:45 Refreshments (508 Math) 9:45-10:00 Registration (412 CEPSR) 10-11 Davar Koshnevisan (412 CEPSR) 11-11:15 Bathroom Break 11:15-12:15 Tianyi Zheng (412 CEPSR) 12:15-1:45pm Lunch (Around Campus) 1:45-2:45 Short Talks (412 CEPSR) 2:45-3:30 Tea (508 Math) 3:30-4:30 Short Talks (412 CEPSR)

Location for the talks will be Columbia University, Davis Auditorium (412 CEPSR), see http://www.cs.columbia.edu/theory/directions.html and all refreshments will be the Mathematics Building, Room 508 (the Cantor Lounge).

**Short talks**

**Thursday 2-2:45pm**

Douglas Dow (NYU), *Joint Localization in Directed Polymers*

Evan Sorensen (Wisconsin), *The stationary horizon and semi-infinite geodesics in the directed landscape*

Ran Tao (Maryland), *Weak convergence of the two-dimensional KPZ equation*

Matthew Nicoletti (MIT), *DimerT model fluctuations via t-embeddings
*

**Thursday 3-4:00pm**

Eren Can Kizildag (Columbia),

*Algorithms and Barriers in the Symmetric Binary Perceptron Model*

Asher Roberts (CUNY),

*The Rate of Convergence for Selberg’s Multivariate Central Limit Theorem*

Eric Thoma (NYU),

*Overcrowding Estimates for the Coulomb Gas*

Tatiana Brailovskaya (Princeton),

*Universality and matrix concentration inequalities*

**Thursday 4:45-6pm**

Lukas Wessels (Georgia Tech./TU Berlin),

*Peng’s Maximum Principle for SPDEs*

Grigory Terlov (UIUC),

*Stein’s method for conditional central limit theorem*

Lane Chun Yeung (Columbia),

*A non-asymptotic perspective on mean field control*

Marco Carfagnini (UCSD),

*Spectral Gap Bounds on H-Type Groups*

Tianle Liu (Tyler) (Harvard),

*Wasserstein-p Bounds for the Central Limit Theorem under Weak Dependence*

Zoraida Fernandez Rico (Columbia),

*Robust bounds on statistical estimation under heavy tails*

**Friday 1:45-2:45pm**

Ruixuan Zhang (Kansas), *Asymptotics of the one-point distribution of the KPZ fixed point conditioned on a large height at an earlier point*

Hindy Drillick (Columbia), *The t-PNG model*

Zhengye Zhou (Texas A&M), *Orthogonal polynomial dualities of multi-species ASEP and related* *processes via the *-bialgebra structure of quantum groups*

Jeffrey Kuan (Texas A&M), *Shift invariance for the multi–species $q$–TAZRP on the infinite line.*

Roger Van Peski (MIT), *Universal random groups and matrix products*

**Friday 3:30-4:30pm**

Kesav Krishnan (UIUC), *Phase Transition in the Discrete Nonlinear Schrodinger Equation*

Graeme Baker (Princeton), *When a supercooled liquid meets a superheated solid*

Emily Dautenhahn (Cornell), *An overview of some heat kernel estimates on manifolds*

Jorge Víquez-Bolaños (Georgia Tech.), *On the Functional Lévy-Itô Stochastic Calculus*

Daniel Slonim (Virginia), *A zero-one law for 2D random walks in random environments with bounded jumps*

**Dinner run by Women in Probability**

There will be a special dinner on Wednesday November 16 accompanying the seminar. It will be organized by Women in Probability http://womeninprobability.org/. Anyone interested in joining should contact Tai Melcher at melcher@virginia.edu.

**Short talks by junior participants**

Junior participants (graduate students and postdocs) are encouraged to apply to give short talks. The link for application is https://forms.gle/x6TeS7sJR9LdMAS29 and the deadline is October 1.

**Financial support**

The Northeast Probability Seminar is supported by the NSF grant.

The grant allows us to offer some financial support to participants from US Universities. We will give preference to graduate students, postdocs, women and minorities, and junior faculty.

Applicants for this financial support should fill the application for funding.

– a one-page letter explaining their interest in the seminar and its relation to their research interests

– a current CV

– graduate students and postdocs should also arrange for a letter of recommendation to be sent to Ivan.Matic@baruch.cuny.edu from their advisor or some expert familiar with their work.

Anyone who is in need of childcare should contact the organizers to receive information about options around Columbia.

For more information, please contact:

Ivan Corwin ivan.corwin@gmail.com OR Milind Hegde mh4259@columbia.edu

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18th Northeast Probability Seminar, 2019

17th Northeast Probability Seminar, 2018

16th Northeast Probability Seminar, 2017

15th Northeast Probability Seminar, 2016

14th Northeast Probability Seminar, 2015

13th Northeast Probability Seminar, 2014

12th Northeast Probability Seminar, 2013

11th Northeast Probability Seminar, 2012

10th Northeast Probability Seminar, 2011

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8th Northeast Probability Seminar, 2009

7th Northeast Probability Seminar, 2008

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5th Northeast Probability Seminar, 2006

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