# Random Matrix & Probability Theory Seminar

As the seminar will not occur on a regular weekly basis, the list below will reflect the dates of the scheduled talks. Room numbers and times will be announced as the details are confirmed

The schedule will be updated as details are confirmed.

 Date………… Name……………. Title/Abstract 2-16-2018 3:30pm G02 Reza Gheissari (NYU) Dynamics of Critical 2D Potts Models Abstract: The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist. We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$. 2-23-2018 3:30pm G02 Mustazee Rahman (MIT) On shocks in the TASEP Abstract: The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers’ equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory. For the curious, here is a video of the shock forming in Burgers’ equation: https://www.youtube.com/watch?v=kU91ciSkmwY