Sourav Chatterjee (Stanford)  

Title: On the decay of correlations in the random field Ising model
Abstract: In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has decay of correlations at any temperature. The proof is ergodic-theoretic in nature and does not provide any quantitative information about the rate of decay. I will present the proof of the first quantitative version of the Aizenman-Wehr theorem. Open questions will be discussed.

Hugo Duminil-Copin (IHES) 

Title: Sharpness of the phase transition via randomized algorithms.
Abstract: We will present a novel technique enabling us to prove that correlations of classical models of statistical physics decay exponentially fast in the subcritical regime. The strategy, relying on randomized algorithms, extends to a variety of models, including continuum percolation models, Ising and Potts models.

Tai Melcher (Virginia)  

Title: Abstract Wiener groups
Abstract: Gaussian measure has for decades been recognized as the appropriate measure to use in infinite-dimensional analysis, and calculus on such measure spaces has become a valuable tool in the analysis of stochastic processes and their applications. For infinite-dimensional curved spaces, the analogue of Gaussian measure is heat kernel measure. We’ll discuss heat kernel measures in a special class of infinite-dimensional spaces and provide motivation for the construction. In particular, these spaces admit a natural hypoelliptic structure, and we’re able to show smoothness results for heat kernel measures under both elliptic and hypoelliptic conditions. Parts of this talk are based on joint work with Fabrice Baudoin, Daniel Dobbs, Bruce Driver, Nate Eldredge, and Masha Gordina.

Perla Sousi (Cambridge)  

Title: Random walk on dynamical percolation
Abstract: We study the behaviour of random walk on dynamical percolation. In this model, the edges of a graph are either open or closed and refresh their status at rate μ, while at the same time a random walker moves on G at rate 1, but only along edges which are open. On the d-dimensional torus with side length n, when the bond parameter is subcritical,  the mixing times for both the full system and the random walker were determined by Peres, Stauffer and Steif. I will talk about the supercritical case, which was left open, but can be analysed using evolving sets (joint work with Y. Peres and J. Steif).

Junior participant talks:

Thursday
2:45PM – Guillaume Dubach (The overlaps between Ginibre eigenvectors).
3:00PM – Erik Bates (Low-temperature localization of directed polymers).
3:15PM – Promit Ghosal (A tale of lower tail of the KPZ equation).
3:30PM – Julian Gold (Scaling limit for Glauber dynamics on the DGFF at low temperatures).
Break
4:00PM: Andrey Sarantsev (Brownian particles interacting through their ranks).
4:15PM – Swee Hong (Random walks with local memory on the square lattice).
4:30PM – Marcus Michelen (Invasion percolation on Galton-Watson trees).
4:45PM – Joshua Rosenberg (Percolation models on supercritical Galton-Watson trees).
5:00PM – Kim Weston  (Financial equilibrium with transaction costs).

Friday
2:15PM – Ning Ning (The tightness of the Kesten-Stigum reconstruction bound for asymmetric model with multiple mutations).
2:30PM – Wenjian Liu (Large degree asymptotics and the reconstruction threshold of Asymmetric Ising Model on regular d-ary trees).
2:45PM – Yanghui Liu (Weighted and unweighted limit theorems).
3:00PM – Qi Feng (Quasi-invariance of horizontal Wiener measure on a compact foliated manifold).
Break
3:45PM – Patricia Alonso Ruiz (Diffusion processes on inverse limit spaces).
4:00PM – Phanuel Mariano (Gradient bounds for general Kolmogorov diffusions using coupling).
4:15PM – Jing Wang (Small time behaviors of degenerate diffusion processes).
4:30PM – Sixian Jin (Series representations of Martingales using Malliavin calculus).

Consult the Columbia Math Department web site http://www.math.columbia.edu/department/probability/nep17/NEP17.html for updates regarding the schedule, a seminar dinner Thursday evening, and accommodations in New York City.