Student Probability Seminar

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Planting trees in log-correlated fields

Speaker: Yujin Kim, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 6, 2023, 1:15 p.m.

Synopsis:

Abstract: This talk concerns the world of log-correlated fields (LCFs) and their extrema, an area born from similarities observed in statistical physics, finance, and biology. Examples in mathematics come from random matrix theory, spin glasses, 2D random surfaces, number theory, and reaction-diffusion PDEs. Though LCFs are strongly-correlated stochastic processes, there have been major breakthroughs in both the math and physics literature that point to conjectural universal behavior for their extremes (as in the case of iid variables, which is essentially a completed theory). Branching Brownian motion (BBM)/random walk (BRW) has served as a paradigmatic model in the field, as great success has been found by uncovering hidden tree structures in the LCF of interest and then making comparisons to BBM/BRW. In this talk, we will develop the theory of the extrema of BBM/BRW and use it to study the extrema of the 2D discrete Gaussian free field.