Mathematics Colloquium

Nonlinear PDEs, random walk, Gaussian processes, random matrices

Speaker: Ofer Zeitouni, NYU and Weizmann Institute

Location: Warren Weaver Hall 1302

Date: Monday, October 22, 2018, 3:45 p.m.


The solution to the one dimensional Fisher-KPP equation (1937) $u_t=frac12 u_{xx}+u(1-u)$  starting from a step initial condition, converges after centering by $2t-\frac32 \logt$ to a traveling wave.  The logarithmic correction term, and in particular the coefficient $3/2$, was computed by Bramson (1978), through a connection with the maximum of branching Brownian motion.  Recently, this computation proved crucial in the solution of a variety of problems: the law of the maximum of the critical Gaussian free field, the cover time of the 2-sphere by Brownian sausage, the maxima of the characteristic polynomials of random matrices, and even the values of the Riemann zeta function on the critical line.  These problems all share a hidden logarithmic (i.e., multiscale) correlation.  In the talk, I will describe these developments and will emphasize the common philosophy in studying these very different models.