# 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