JournalsowrVol. 10, No. 2pp. 1205–1251

Extremes in Branching Random Walk and Branching Brownian Motion

  • Louigi Addario-Berry

    McGill University, Montreal, Canada
  • Nathanaël Berestycki

    University of Cambridge, United Kingdom
  • Nina Gantert

    TU München, Garching bei München, Germany
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Abstract

Branching random walk (BRW) and branching Brownian motion (BBM) are mathematical models for population growth and spatial displacement. When resources are plentiful, population sizes grow exponentially in time. In such a situation, exceptional (or extreme) individuals will be found far from the bulk of the population. The study of such individuals, and their ancestral lineages, was the subject of the workshop. On one hand, this is a classical topic, with well-known connections to the KPP-equation and to search algorithms. On the other hand, substantial recent developments have recently been obtained via new approaches to the subject (stopping lines and spines, the view from the tip, multivariate analytic combinatorics), or from researchers working in seemingly distinct areas (from stochastic partial differential equations to theoretical physics).

Cite this article

Louigi Addario-Berry, Nathanaël Berestycki, Nina Gantert, Extremes in Branching Random Walk and Branching Brownian Motion. Oberwolfach Rep. 10 (2013), no. 2, pp. 1205–1251

DOI 10.4171/OWR/2013/20