Minima in branching random walks

Abstract

Given a branching random walk, let Mn be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{|Mn−EMn|>x}, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89–108], our results fully characterize the possible behavior of EMn when the branching random walk has bounded branching and step size.

Locations

• The Annals of Probability - View - PDF
• arXiv (Cornell University) - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View
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