Oberwolfach Reports

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Volume 10, Issue 2, 2013, pp. 1205–1251
DOI: 10.4171/OWR/2013/20

Published online: 2014-03-17

Extremes in Branching Random Walk and Branching Brownian Motion

Louigi Addario-Berry[1], Nathanaël Berestycki[2] and Nina Gantert[3]

(1) McGill University, Montreal, Canada
(2) University of Cambridge, United Kingdom
(3) TU München, Garching bei München, Germany

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).

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Addario-Berry Louigi, Berestycki Nathanaël, Gantert Nina: Extremes in Branching Random Walk and Branching Brownian Motion. Oberwolfach Rep. 10 (2013), 1205-1251. doi: 10.4171/OWR/2013/20