CUNY Probability Seminar, Fall 2017

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

Ivan Matic (maticivan at gmail dot com)

Tuesday, September 12, 2017, 4:15 PM, Rm. 5417

Speaker: Jack Hanson, City College, CUNY

Title: The chemical distance in 2d critical percolation

Abstract: In 2d critical percolation, a fraction 1/2 of edges are removed from Z^2, and one considers the resulting subgraph. The intrinsic or “chemical” distance in this graph is known to grow superlinearly in the Euclidean distance. For instance, the length S_n of the shortest crossing of a sidelength n square is typically at least n^{1+\delta}. A trivial upper bound is provided by L_n, the length of the lowest crossing of the square; on the triangular lattice, L_n scales as n^{4/3}. We will discuss work providing the first nontrivial power law improvement to this upper bound, showing in particular that E[S_n] < n^{-\delta} E[L_n].

Tuesday, September 26, 2017, 4:15 PM, Rm. 5417

Speaker: Atilla Yilmaz, NYU and Koc University

Title: Nonconvex homogenization of a class of one-dimensional stochastic viscous Hamilton-Jacobi equations

Abstract: I will present a homogenization result for a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs have representations involving exponential expectations of controlled Brownian motion in random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and it turns out to be explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in random potential. The proof of homogenization relies on identifying asymptotically optimal control policies and constructing correctors from the PDE perspective. Based on recent joint work with Elena Kosygina and Ofer Zeitouni.

Tuesday, October 3, 2017, 4:15 PM, Rm. 5417

Speaker: Toby Johnson, College of Staten Island

Title: TBA

Abstract: TBA

Tuesday, October 10, 2017, 4:15 PM, Rm. 5417

Speaker: Joe Po-Chou Chen, Colgate University

Title: TBA

Abstract: TBA

Tuesday, November 7, 2017, 4:15 PM, Rm. 5417

Speaker: Thomas Leble, NYU

Title: TBA

Abstract: TBA