# 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

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

The Fourteenth Northeast Probability Seminar (NEPS) will be held at NYU’s Kimmel Center (Room 912/914) on November 19th and Room 109 of the Courant Institute, NYU, on November 20th, 2015.

Details
The invited speakers are:

• 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