*Shirshendu Chatterjee *(shirshendu at ccny dotcuny dotedu)

**Tuesday, February 7, 4:15 PM, Rm. 5417**

Speaker: Christian Benes, Brooklyn College, CUNY

Title: Where Planar Simple Random Walk Loses its Rotational Symmetry

Abstract: We present an explicit local limit theorem for simple random walk in dimensions 1 and 2, valid for all points in the range of the walk. The two-dimensional result allows to obtain a precise description of where and how planar simple random walk loses its approximate rotational symmetry.

**Tuesday, February 21, 4:15 PM, Rm. 5417**

Speaker: Daniel Ahlberg, IMPA, Brazil

Title: Random coalescing geodesics in first-passage percolation

Abstract: A random metric on is obtained by assigning non-negative i.i.d. weights to the edges of the nearest neighbour lattice. We shall discuss properties of geodesics in this metric. We develop an ergodic theory for infinite geodesics via the study of what we shall call `random coalescing geodesics’. Random coalescing geodesics have a range of nice properties. By showing that they are (in some sense) dense is the space of geodesics, we may extrapolate these properties to all infinite geodesics. As an application of this theory we answer a question posed by Benjamini, Kalai and Schramm in 2003, that has come to be known as the `midpoint problem’. This is joint work with Chris Hoffman.

**Tuesday, February 28, 4:15 PM, Rm. 5417**

Speaker: Warren Tai, Graduate Center, CUNY

Title: Is the Riemann zeta function in a short interval a 1-RSB spin glass?

Abstract: Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.

**Tuesday, March 7, 4:15 PM, Rm. 5417**

Speaker: Guillaume Barraquand, Columbia University

Title: ASEP on the positive integers with an open boundary.

Abstract: The asymptotic fluctuations of a large class of growth processes and one dimensional particle systems are predicted to follow probability distributions from random matrix theory with 1/3 scaling exponents. It is conjectured that the limit theorems are universal, in the sense that they do not depend on the microscopic details of the model. However, the geometry and boundary conditions have an influence on the nature of limiting statistics. In this talk, we will explore the situation in a half space. We will recall the general predictions for such systems and present new results about the asymmetric simple exclusion process when particles travel on the positive integers coming out of a reservoir at the origin. Joint work with Alexei Borodin, Ivan Corwin and Michael Wheeler.

**Tuesday, March 14, 4:15 PM, Rm. 5417**

**The seminar is canceled because of an unavoidable circumstance.**

Speaker: Victor de la Peña, Columbia University, Department of Statistics

Title: On Boundary Crossing By Stochastic Processes

Abstract: In this talk, we introduce an approach to bound the expected time for stochastic processes to cross a boundary. The approach can be thought as a direct extension of the concept of boundary crossing of non-random functions to that of stochastic processes. It can also be viewed as an extension of Wald’s equations in sequential analysis to the case of stochastic processes with arbitrary dependence structure.

**Tuesday, March 21, 4:15 PM, Rm. 5417**

Speaker: Kei Kobayashi, Fordham University

Title: Stochastic differential equations modeling anomalous diffusions

Abstract: Standard Brownian motion composed with the inverse of a stable subordinator has been used to model a subdiffusion, which is a type of an anomalous diffusion where particles spread more slowly than the classical Brownian particles. This new stochastic process is significantly different from the Brownian motion; for example, it is neither Markovian nor Gaussian and has transition probabilities satisfying a time-fractional order heat equation.

This talk focuses on stochastic differential equations (SDEs) driven by a L\’evy process composed with the inverse of a stable subordinator. We derive time-fractional Kolmogorov-type equations associated with the SDEs as well as justify the effectiveness of a numerical approximation scheme for the SDEs. This is joint work with Molly Hahn, Ernest Jum and Sabir Umarov.

**Tuesday, March 28, 4:15 PM, Rm. 5417**

Speaker: Konstantin Tikhomirov, Princeton University

Title: The spectral radius of a random matrix with heavy-tailed entries

Abstract: Consider a square matrix with independent and identically

distributed entries of zero mean and unit variance. It is well known

that if the entries have a finite fourth moment, then, in high

dimension, with high probability, the spectral radius is close to the

square root of the dimension. We conjecture that this holds true under

the sole assumption of zero mean and unit variance, in other words

that there are no outliers in the circular law. In this work we

establish the conjecture in the case of symmetrically distributed

entries with a finite moment of order larger than two. The proof uses

the method of moments combined with a novel truncation technique for

cycle weights that might be of independent interest. This is a joint

work with Charles Bordenave, Pietro Caputo and Djalil Chafaï.

**Tuesday, April 4, 4:15 PM, Rm. 5417**

Speaker: Martin Zerner, University of Tuebingen

Title: Recurrence and transience of contractive autoregressive

processes and related Markov chains

Abstract: We characterize recurrence and transience of nonnegative

multivariate autoregressive processes of order one with random

contractive coefficient matrix, of subcritical multitype Galton-Watson

branching processes in random environment with immigration, and of the

related max-autoregressive processes and general random exchange

processes. Our criterion is given in terms of the maximal Lyapunov

exponent of the coefficient matrix and the cumulative distribution

function of the innovation/immigration component.

**Tuesday, May 2, 4:15 PM, Rm. 5417**

Speaker: Matthew Junge, Duke University

Title: The bullet problem with discrete speeds

Abstract: A bullet is fired along the real line each second with independent uniformly random speeds from [0,1]. When two bullets collide they mutually annihilate. The still open bullet problem asks if the first bullet ever survives. We establish survival in the variant where speeds are discrete. Joint with Brittany Dygert, Christoph Kinzel, Annie Raymond, Erik Slivken, and Jennifer Zhu.

**Tuesday, May 9, 4:15 PM, Rm. 5417**

Speaker: Moumanti Podder, Courant Institute, NYU

Title: Rogue Fixed Points of Tree Automata on Galton-Watson Trees

Co-authors: Joel Spencer, Tobias Johnson and Fiona Skerman

Abstract: This talk will focus on tree automata, which are tools to analyze existential monadic second order properties of rooted trees. A tree automaton consists of a finite set of colours, and a map . Given a rooted tree and a colouring , we call compatible with automaton if for every , we have , where and is the number of children of with colour . Under the Galton-Watson branching process set-up, if denotes the probability that a node is coloured , then is obtained as a fixed point of a system of equations. But this system need not have a unique fixed point.

Our question attempts to answer whether a fixed point of such a system simply arises out of analytic reasons, or if it admits of a probabilistic interpretation. I shall formally define *interpretation*, and provide a nearly complete description of necessary and sufficient conditions for a fixed point to *not* admit an interpretation, in which case it is called *rogue*.

]]>Attention: You need to have a picture ID to be allowed to enter the conference building.

**Morning Session:** Chair, Carl Mueller (University of Rochester)

9:00 – 10:00 am Registration, light refreshments

9:45 – 10:00 am Greetings: Dean Aldemaro Romero

10:00 – 11:00 am **Vincent Vargas** (Ecole Normale Superieure de Paris)

*Ward and Belavin-Polyakov-Zamolodchikov (BPZ) identities for Liouville quantum field theory on the Riemann sphere *

11:00 – 11:30 pm break

11:30 – 12:30 pm **Sandrine Péché** (Université Paris Diderot)

*Some results on delocalization and localization of eigenvectors of random matrices*

12:30 – 02:15 pm Lunch break

**Afternoon Session: **Chair, Louis-Pierre Arguin (CUNY)

2:15 – 3:15 pm 10-15 minute informal talks and discussion, including:

2:15 – 2:30 pm** Qi Feng** (University of Connecticut):* On a priori estimates for rough PDEs *

2:30 – 2:45 pm **Phanuel Mariano **(University of Connecticut): *Coupling on the Heisenberg group and its applications to gradient estimates*

2:45 – 3:00 pm **Debapratim Banerjee** (University of Pennsylvania): *Contiguity results for planted partition models: the dense case*

3:00 – 3:15 pm **Zichun Ye** (UBC): *Models of Gradient Type with Sub-Quadratic Actions*

3:15 – 3:30 pm break

3:30 – 4:45 pm 10-15 minute informal talks and discussion, including:

3:30 – 3:45 pm **Konstantinos Karatapanis** (University of Pennsylvania): One dimensional system arising in stochastic gradient descent

3:45 – 4:00 pm **Dan Han **(University of North Carolina, Charlotte): *Branching random walks with immigration
*4:00 – 4:15 pm

4:30 – 4:45 pm

4:45 – 5:45 **Conference Reception
**Adjacent to Room 750

6:15 – **Conference Dinner
**Turkish kitchen, 386 Third Ave, (between 27’th and 28’th Streets)

**Friday, Nov. 18th, **Room 750 of the Baruch College Conference Center, CUNY

151 East 25th street (between Lexington Ave and 3rd Ave)

**Morning Session:** Chair,** ** Daniel Ocone (Rutgers)

9:00 – 9:30 am Registration, light refreshments

9:30 – 10:30 am **Balint Virag** (University of Toronto)

*Random relaxed sorting networks*

10:30 – 11:00 am break

11:00 – 12:00 **Nike Sun** (University of California, Berkeley)

*Phase transitions in random constraint satisfaction problems*

12:00 – 1:30 pm Lunch break

**Afternoon Session:** Chair, Nayantara Bhatnagar (University of Delaware)

1:30 – 2:30 pm 10-15 minute informal talks and discussion, including:

1:30 – 1:45 pm** Chen Xu** (Georgia Institute of Technology): *Concentration of geodesics in directed Bernoulli percolation*

1:45 – 2:00 pm **Alisa Knizel **(MIT): *Asymptotics of random domino tilings of rectangular Aztec diamonds*

2:00 – 2:15 pm **Mickey Salins** (Boston University): *Rare event simulation via importance sampling for linear SPDEs*

2:15 – 2:30 pm **Zhipeng Liu **(NYU): *Height fluctuations of stationary TASEP on a ring in relaxation time scale*

**Participants
**Louis-Pierre Arguin, CUNY

Yuri Bakhtin, NYU

Debapratim Banerjee, University of PA

Guillaume Barraquand, Columbia

Christian Benes, CUNY

Lucas Benigni, NYU

Nayantara Bhatnagar, Univ of DE

Paul Bourgade, NYU

Milan Bradonjic, Bell Lab

Zhiqi Bu, Columbia

Michael Carlisle, CUNY

Omar Chakhtoun, CUNY

Ivan Corwin, Columbia

Berend Coster, University of Connecticut

Victor De la Pena, Columbia

Julien Dubedat, Columbia

Shum Fanny, NYU

Qi Feng, Univ of Ct

Antonia Foldes, CUNY

Patricia Garmirian, Tufts University

Janusz Golec, Fordham

Yu Gu, Standford

Olympia Hadjiliadis, CUNY

Dan Han, Univ of NC at Charlotte

Jack Hanson, CUNY

Lisa Hartung, NYU

Vivian Healey, Brown University

Tiefeng Jiang, U of Minnesota

Tobias Johnson, NYU

Konstantinos Karatapanis, University of PA

Ioannis Karatzas, Columbia

George Kerchev, GA Inst of Tech

Yuri Kifer, University of PA

Alisa Knizel, MIT

Kei Kobayashi, Fordham

Elena Kosygina, CUNY

SangJoon Lee, Univ of CT

Liying Li, NYU

Janna Lierl, Univ of CT

Kevin Lin, Univ of Rochester

Zhipeng Liu, NYU

Eyal Lubetzky, NYU

Jessica Maghakian, Rockefeller University

Phanuel Mariano, Univ of Connecticut

Nevena Maric, Univ of MO St Louis

Ivan Matic, CUNY

Olive Mbianda, University of Minnesota Duluth

Benjamin Mckenna, NYU

Marcus Michelen, University of PA

Sevak Mketchyan, Rocheaster

Carl Mueller, Univ of Rochester

Mihai Nica, NYU

Daniel Ocone, Rutgers

Zsolt Pajor-Gyulai, NYU

Greta Panova, University of PA

Sandrine Peche, Univ of Paris

Dan Pirjol, Industry

Madan Puri, Indiana University

Junqing Qian, University of Connecticut

Brian Rider, Temple

Jay Rosen, CUNY

Josh Rosenberg, University of PA

Mickey Salins, Boston Univ

Donghyun Seo, NYU

Insuk Seo, UC Beerkely

Leila Setayeshgar, Providence College

Nike Sun, Berkeley

Yi Sun, Columbia

Warren Tai, CUNY

Li-Cheng Tsai, Columbia

Yannis Tziligakis, Ventrisk

S R S Varadhan, NYU

Vincent Vargas, ENS

Balint Virag, Univ of Toronto

Tianqi Wu, NYU

Wei Wu, NYU

Chen Xu, GA Inst of Tech

Kevin Xu, Columbia

Zichun Ye, UBC

Attention: You need to have a picture ID to be allowed to enter the conference building.

**Morning Session:** Chair, S.R.Srinivasa Varadhan (Courant Institute)

9:00 – 10:00 am Registration, light refreshments

10:00 – 11:00 am **Jean- François Le Gall** (University Paris-Sud Orsay)

11:00 – 11:30 pm break

11:30 – 12:30 pm **Mykhaylo Shkolnikov** (Princeton University)

*Edge of beta ensembles and the stochastic Airy semigroup*

12:30 – 02:15 pm Lunch break

**Afternoon Session: **Chair, Daniel Ocone (Rutgers, The State University of New Jersey)

2:15 – 3:15 pm 10-15 minute informal talks and discussion, including:

2:15 – 2:30 pm** Yu Gu** (Stanford):* Scaling limits in stochastic homogenization*

2:30 – 2:45 pm **Qi Feng **(Purdue): *Log-Sobolev inequalities on the horizontal path space of a totally
geodesic foliation *

2:45 – 3:00 pm

3:00 – 3:15 pm

3:15 – 3:30 pm break

3:30 – 4:30 pm 10-15 minute informal talks and discussion, including:

3:30 – 3:45 pm **Andrey Sarantsev** (UC Santa Barbara): *Infinite systems of competing Brownian particles*

3:45 – 4:00 pm **Jiange Li **(Delaware): *Optimal concentration of information content under convex measures*

4:00 – 4:15 pm** Reza Gheissari** (NYU): *Conformal invariance and lattice fields of the Ising model *

4:15 – 4:30 pm** Eyal Neuman** (Rochester): *Discrete SIR Epidemic Processes and their Relation to Extreme Values of Branching Random Walk*

4:45 – 5:45 **Conference Reception
**Courant Institute, 13th Floor Lounge

6:00 – **Conference Dinner **

**Friday, Nov. 20th, **Room 109 of the Courant Institute, NYU

**Morning Session:** Chair, Ivan Corwin (Columbia University)

9:00 – 9:30 am Registration, light refreshments

9:30 – 10:30 am **Francis Comets** (Université Paris Diderot)

*Localization in one-dimensional log-gamma polymers*

10:30 – 11:00 am break

11:00 – 12:00 **Jian Ding** (University of Chicago)

*Some geometric aspects for two-dimensional Gaussian free fields*

12:00 – 1:45 pm Lunch break

**Afternoon Session:** Chair, Louis-Pierre Arguin (Baruch College, CUNY)

1:45 – 2:45 pm 10-15 minute informal talks and discussion, including:

1:45 – 2:00 pm** Insuk Seo** (NYU): *Large Deviation Principle for Interacting Brownian Motions *

2:00 – 2:15 pm **Joe P. Chen **(UConn): *Current large deviations in the boundary-driven symmetric simple exclusion process on the Sierpinski gasket*

2:15 – 2:30 pm **Mickey Salins** (Boston University): *The Smoluchowski-Kramers approximation and large deviations for the stochastic wave equation*

2:30 – 2:45 pm **Aukosh Jagannath** (NYU): *The Parisi variational problem for mixed p-spin glasses*

2:45 – 3:00 pm break

3:00 – 4:00 pm 10-15 minute informal talks and discussion, including:

3:00 – 3:15 pm **Moumanti Poder** (NYU): *Probability of any given neighborhood of the root, conditioned on the tree being infinite*

3:15 – 3:30 pm **Kei Kobayashi** (UT Knoxville): *Numerical approximation of stochastic differential equations driven by a time-changed Brownian motion*

3:30 – 3:45 pm **Hugo Panzo** (UConn): *The critical regimes of a two-parameter scaled Brownian penalization*

3:45 – 4:00 pm **Zsolt Pajor Gyulai** (NYU): *Dynamical systems perturbed by a diffusion driven by a null-recurrent fast motion*

**Details**

The invited speakers are:

- Jian Ding (University of Chicago)

“Some geometric aspects for two-dimensional Gaussian free fields.” - Francis Comets (Université Paris Diderot)

“Localization in one-dimensional log-gamma polymers” - Jean-François Le Gall (University Paris-Sud Orsay)

“First-passage percolation on random planar graphs.” - Mykhaylo Shkolnikov (Princeton University)

“Edge of beta ensembles and the stochastic Airy semigroup.”

**Please note:**

- Financial support is still available.

**Financial support to attend the conference.**The NSF 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 provide:- 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 from their advisor or some expert familiar with their work

Materials should be sent either by e-mail (preferred) or postal mail to:

Ivan Matic

Department of Mathematics, 6th Floor, Room 6-230

Baruch College of the City University of New York

One Bernard Baruch Way (55 Lexington Ave. at 24th St)

New York, NY 10010

ivan.matic@baruch.cuny.edu - There will be a dinner for women in probability:

*Women in Probability*is an organization for women active in probability research. Our primary purpose is to provide networking and mentoring opportunities for early career women. Our activities are funded by the NSF. For more information on Women in Probability and its activities, please visit our website womeninprobability.org.

Abstracts:

**Jian Ding (University of Chicago)**

“Some geometric aspects for two-dimensional Gaussian free fields”:I will give a review on recent progresses on extreme values of two-dimensional discrete Gaussian free field, including the law of convergence for the centered maximum as well as the universality (for the maximum) among log-correlated Gaussian fields. Then, I will discuss the first passage percolation where the vertex weight is given by exponentiating the field, and present some recent result on the universality (non-universality) on such FPP metric in the class of log-correlated Gaussian field.Based on joint works with Maury Bramson, Subhajit Goswami, Rishideep Roy, Ofer Zeitouni and Fuxi Zhang in various combinations.**Francis Comets (Université Paris Diderot)**

“Localization in one-dimensional log-gamma polymers”:Directed polymers in random environment are known to localize when the disorder is strong. We can analyse this in a precise manner for the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Sepp{\”a}l{\”a}inen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. Joint work with V.-L. Nguyen.**Jean-François Le Gall (University Paris-Sud Orsay)**

“First-passage percolation on random planar graphs”We study local modifications of the graph distance in large random triangulations. Our main results show that, in large scales, the modified distance behaves like a deterministic constant c times the usual graph distance. This applies to the first-passage percolation distance obtained by assigning independent random weights to the edges of the graph. We also consider distances on the dual map, and in particular the first-passage percolation with exponential edge weights, which is closely related to the so-called Eden model. In the latter case, we are able to compute explicitly the constant c. In general however, the constant c is obtained from a subadditivity argument in the infinite half-plane model that describes the asymptotic shape of the triangulation near the boundary of a large ball. Our results apply in particular to the infinite random triangulation known as the UIPT, and show that balls of the UIPT for the first-passage percolation distance are asymptotically close to balls for the graph distance. This is a joint work with Nicolas Curien.**Mykhaylo Shkolnikov (Princeton University)**

“Edge of beta ensembles and the stochastic Airy semigroup”Beta ensembles arise naturally in random matrix theory as a

family of point processes, indexed by a parameter beta, which

interpolates between the eigenvalue processes of the Gaussian

orthogonal, unitary and symplectic ensembles (GOE, GUE and GSE). It is

known that, under appropriate scaling, the locations of the rightmost

points in a beta ensemble converge to the so-called Airy(beta)

process. However, very little information is available on the

Airy(beta) process except when beta=2 (the GUE case). I will explain

how one can write a distribution-determining family of observables for

the Airy(beta) process in terms of a Brownian excursion and a Brownian

motion. Along the way, I will introduce the semigroup generated by the

stochastic Airy operator of Ramirez, Rider and Virag. Based on joint

work with Vadim Gorin.