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An Isaac Newton Institute Workshop

First-Passage and Extreme Value Problems in Random Processes

Tightness for the mim=nimum displacement of branching random walk and some other old problems

26th June 2006

Author: Bramson, M (University of Minnesota)

Abstract

Study of solutions of certain families of semilinear heat equations dates back to Kolmogorov-Petrovsky-Piscounov in 1937; since then this problem has been thoroughly analyzed. Substantially less is known about the behavior of their discrete time analogs; several basic questions have been unresolved since the 1970's. In the probabilistic context, the continuous time problem corresponds to the minimum displacement of branching Brownian motion, and the discrete time problem to the minimum displacement of branching random walk. Here, we summarize this background and present some new results for branching random walk.