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SUMMARY:Michael Damron (Georgia Tech)
DTSTART:20201211T173000Z
DTEND:20201211T183000Z
DTSTAMP:20260423T005654Z
UID:PatC/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/14/">Cr
 itical first-passage percolation in two dimensions</a>\nby Michael Damron 
 (Georgia Tech) as part of Probability and the City Seminar\n\n\nAbstract\n
 In 2d first-passage percolation (FPP)\, we place nonnegative i.i.d. weight
 s (t_e) on the edges of Z^2 and study the induced weighted graph pseudomet
 ric T = T(x\,y) If we denote by p = P(t_e = 0)\, then there is a transitio
 n in the large-scale behavior of the model as p varies from 0 to 1. When p
  < 1/2\, T(0\,x) grows linearly in x\, and when p > 1/2\, it is stochastic
 ally bounded. The critical case\, where p = 1/2\, is more subtle\, and the
  sublinear growth of T(0\,x) depends on the behavior of the distribution f
 unction of t_e near zero. I will discuss my work over the past few years t
 hat (a) determines the exact rate of growth of T(0\,x)\, (b) determines th
 e "time constant" for the site-FPP model on the triangular lattice and\, m
 ore recently (c) studies the growth of T(0\,x) in a dynamical version of t
 he model\, where weights are resampled according to independent exponentia
 l clocks. These are joint works with J. Hanson\, D. Harper\, W.-K. Lam\, P
 . Tang\, and X. Wang.\n
LOCATION:https://researchseminars.org/talk/PatC/14/
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