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Tightness for the minimum displacement of branching random walk and some other old problems

Presented by: 
M Bramson University of Minnesota
Thursday 29th June 2006 - 09:00 to 10:00
INI Seminar Room 1

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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons