The CUNY Probability Seminar will be held by videoconference for the entire semester. Its usual time will be Tuesdays from 4:30 to 5:30 pm EST. The exact dates, times, and seminar links are mentioned below. If you are interested in speaking at the seminar or would like to be added or to be removed from the seminar mailing list, then please contact either of the Seminar Coordinators
Videoconference Link (via Zoom
Time: October 12, 4:30 – 5:30 pm EDT
Title: Chemical distance for 2d critical percolation and random cluster model
Abstract: In 2-dimensional critical percolation, with positive probability, there is a path that connects the left and right side of a square box. The chemical distance is the expected length of the shortest such path conditional on its existence. In this talk, I will introduce the best known estimates for chemical distance. I will then discuss analogous estimates for the radial chemical distance (the expected length of the shortest path from the origin to distance n), as well as recent extensions of these estimates to the random cluster model. A portion of this talk is based on joint work with Philippe Sosoe.
Time: October 19, 3:30 – 4:30 pm EDT
Title: Non-equilibrium multi-scale analysis and coexistence in competing
Abstract: We consider a natural random growth process with competition on Z^d called first-passage percolation in a hostile environment, that consists of two first-passage percolation processes FPP_1 and FPP_\lambda that compete for the occupancy of sites. Initially FPP_1 occupies the origin and spreads through the edges of Z^d at rate 1, while FPP_\lambda is initialised at sites called seeds that are distributed according to a product of Bernoulli measures of parameter p. A seed remains dormant until FPP_1 or FPP_\lambda attempts to occupy it after which it spreads through the edges of Z^d at rate \lambda. We will discuss the results known for this model and present a recent proof that the two types can coexist (concurrently produce an infinite cluster) on Z^d. We remark that, though counterintuitive, the above model is not monotone in the sense that adding a seed of FPP_\lambda could favor FPP_1. A central contribution of our work is the development of a novel multi-scale analysis to analyze this model, which we call a multi-scale analysis with non-equilibrium feedback and which we believe could help analyze other models with non-equilibrium dynamics and lack of monotonicity.
Based on a joint work with Tom Finn (Univ. of Bath).
Time: October 26, 3:30 – 4:30 pm EDT
Time: November 02, 4:30 – 5:30 pm EDT
Time: November 09, 4:30 – 5:30 pm EDT
Title: Cooperative motion random walks
Abstract: Cooperative motion random walks form a family of random walks where each step is dependent upon the distribution of the walk itself. Movement is promoted at locations of high probability and dampened in locations of low probability. These processes are a generalization of the hipster random walk introduced by Addario-Berry et. al. in 2020. We study the process through a recursive equation satisfied by its CDF, allowing the evolution of the walk to be related to a finite difference scheme. I will discuss this relationship and how PDEs can be used to describe the distributional convergence of asymmetric and symmetric cooperative motion. This talk is based on joint work with Louigi Addario-Berry and Jessica Lin.
Time: November 30, 4:30 – 5:30 pm EST
Time: December 07, 4:30 – 5:30 pm EST
Time: August 31, 4:30 – 5:30 pm EDT
Title: Dynamical First-Passage Percolation
Abstract: In first-passage percolation (FPP), we place i.i.d. nonnegative weights on the edges of the cubic lattice Z^d and study the induced weighted graph metric T = T(x,y). Letting F be the common distribution function of the weights, it is known that if F(0) is less than the threshold p_c for Bernoulli percolation, then T(x,y) grows like a linear function of the distance |x-y|. In 2015, Ahlberg introduced a dynamical model of first-passage percolation, in which the weights are resampled according to Poisson clocks, and considered the growth of T(x,y) as time varies. He showed that when F(0) < p_c, the model has no “exceptional times” at which the order of the growth is anomalously large or small. I will discuss recent work with J. Hanson, D. Harper, and W.-K. Lam, in which we study this question in two dimensions in the critical regime, where F(0) = p_c, and T(x,y) typically grows sublinearly. We find that the existence of exceptional times depends on the behavior of F(x) for small positive x, and we characterize the dimension of the exceptional sets for all but a small class of such F.
Time: September 14, 4:30 – 5:30 pm EDT
Title: Pandemic REUs
Abstract: The pandemic changed many things, REU Programs included. I will discuss challenges and advantages of mentoring undergraduates in math research from afar. Some results about interacting particle systems—namely, the frog model and ballistic annihilation—from this summer will also be presented.
Time: October 05, 4:30 – 5:30 pm EDT
Speaker: David Aldous,
Professor, Emeritus and Professor of the Graduate School, UC Berkeley
Title: Two processes on compact spaces
Abstract: It can be found here.