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10th Northeast Probability Seminar

CUNY Probability Seminar, Spring 2018

The CUNY Probability Seminar is typically held on Tuesdays from 4:15 to 5:15 pm at the CUNY Graduate Center Math Department. The exact dates, times and locations are mentioned below. If you want to talk at the seminar, or want to be added to/removed from the seminar mailing list, then please contact the Seminar Coordinator

Jack Hanson (http://jhanson.ccny.cuny.edu/)

Tuesday, February 6, 2018, 4:15 PM, Rm. 3307:

Speaker: Joshua Rosenberg, UPenn

Title: Invasion Percolation on Galton-Watson Trees

Abstract: This talk will focus on invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for almost every Galton-Watson tree, invasion percolation induces a probability measure on infinite paths from the root. I will discuss our proof demonstrating that under certain conditions of the progeny distribution, this measure is absolutely continuous with respect to the limit uniform measure. This confirms that invasion percolation, an efficient self-tuning algorithm, may be used to sample approximately from the limit uniform distribution. Time permitting, I will also discuss a related result we achieved which involved proving a limit law for the forward maximal weights along the backbone of the invasion cluster. This is based on joint work with Marcus Michelen and Robin Pemantle.

Tuesday, February 13, 4:15 PM, Rm. 3307:

Speaker: Jay Rosen, CUNY (College of Staten Island)

Title: Tightness for the Cover Time of compact two dimensional manifolds

Abstract: Let $\CC^\ast_{\ep,M}$ denote the cover
time of the two dimensional compact manifold $M$ by
a Wiener sausage of radius $\ep$. We prove that
$$\sqrt{\CC^{\ast}_{\ep,M} }
-\sqrt{\frac{2A_{M}}{\pi}}$\log \ep^{-1}-\frac14\log\log \ep^{-1}$$$ is tight, where $A_{M}$ denotes the Riemannian area of $M$.

Joint work with David Belius and Ofer Zeitouni

Tuesday, April 10, 4:15 PM, Rm. 3307:

Speaker: Arjun Krishnan, U. of Rochester

Title: Stationary coalescing walks on the lattice

Abstract: Consider a measurable dense family of semi-infinite nearest-neighbor paths on the integer lattice in d dimensions. Assuming that they do not have loops and cross an infinite family of parallel planes, we completely classify their collective behavior in d=2. We use our theory to classify the behavior of semi-infinite geodesics in random translation invariant metrics on the lattice; it applies, in particular, to first- and last-passage percolation. (joint work with Jon Chaika)

Tuesday, April 17, 4:15 PM, Rm. 3307:

Speaker: Philippe Sosoe, Cornell University

Title: Dispersive equations with random initial data

Abstract: Beginning the 1980s, there has been interest in considering certain classical nonlinear equations such as nonlinear Schroedinger, Korteweg de Vries and wave equations, with random initial data. I will explain the motivation for this setting, describe some of the results obtained by using probabilistic methods for dispersive nonlinear equations, and finish by describing some recent and ongoing work by myself and collaborators on the subject.

Tuesday April 24, 4:15 PM, Rm. 3307

Speaker: Guillaume Dubach

Title: Eigenvectors of non-hermitian random matrices

Abstract: Eigenvectors of non-hermitian matrices are non-orthogonal, and their distance to a unitary basis can be quantified through the matrix of overlaps. These variables quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. They first appeared in the physics literature; well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices. For the same model, we extend their results by deriving the distribution of the overlaps and their correlations. (Joint work with P. Bourgade)

Tuesday May 1, 4:15 PM, Rm. 3307

Speaker: Matthew Junge, Duke U.

Title: Chase-Escape

Abstract: Imagine barnacles and mussels spreading across the surface of a rock. Barnacles move to adjacent unfilled spots. Mussels too, but they can only attach to barnacles. Barnacles with a mussel on top no longer spread. What conditions on the rock geometry (i.e. graph) and spreading rates (i.e. exponential clocks) ensure that barnacles can survive? Chase-escape can be formalized in terms of competing Richardson growth models; one on top of the other. New, tantalizing open problems will be presented. Joint work with Rick Durrett and Si Tang.

Tuesday May 15, 4:15 PM, Rm. 3307

Speaker: Sixian Jin, Fordham U.

Title: TBA

Abstract: TBA

CUNY Probability Seminars Spring 2017

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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 $Z^2$ 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 $A$ consists of a finite set $\Sigma$ of colours, and a map $\Gamma: \mathbb{N}^{\Sigma} \rightarrow \Sigma$ . Given a rooted tree $T$ and a colouring $\omega: V(T) \rightarrow \Sigma$ , we call $\omega$ compatible with automaton $A$ if for every $v \in V(T)$ , we have $\omega(v) = \Gamma(\vec{n})$ , where $\vec{n} = (n_{\sigma}: \sigma \in \Sigma)$ and $n_{\sigma}$ is the number of children of $v$ with colour $\sigma$ . Under the Galton-Watson branching process set-up, if $p_{\sigma}$ denotes the probability that a node is coloured $\sigma$ , then $\vec{p} = (p_{\sigma}: \sigma \in \Sigma)$ 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.

15th Annual Northeast Probability Seminar (Nov 17-18, 2016) Schedule

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Thursday, Nov. 17th, Room 750 of the Baruch College Conference Center, CUNY
151 East 25th street (between Lexington Ave and 3rd Ave)

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 Kevin Lin (University of Rochester): Hitting Properties of the Stochastic Wave Equation
4:15 – 4:30 pm Vivian Healey (Brown University): Embedding Galton-Watson Trees using the Loewner Equation
4:30 – 4:45 pm Josh Rosenberg (University of Pennsylvania): The frog model with drift on R

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

14th Annual Northeast Probability Seminar (Nov 19-20, 2015) Schedule

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Thursday, Nov. 19th , Room 912/914 of the Kimmel Center at NYU

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)
First-passage percolation on random planar graphs

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 Konstantin Matveev (Harvard): $q$-randomized RSK’s and random polymers
3:00 – 3:15 pm Fan Ny Shum (UConn): Stabilization by noise of a $C^2$-valued coupled system

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