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May 2009 Minima in branching random walks
Louigi Addario-Berry, Bruce Reed
Ann. Probab. 37(3): 1044-1079 (May 2009). DOI: 10.1214/08-AOP428

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{|MnEMn|>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.

Citation

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Louigi Addario-Berry. Bruce Reed. "Minima in branching random walks." Ann. Probab. 37 (3) 1044 - 1079, May 2009. https://doi.org/10.1214/08-AOP428

Information

Published: May 2009
First available in Project Euclid: 19 June 2009

zbMATH: 1196.60142
MathSciNet: MR2537549
Digital Object Identifier: 10.1214/08-AOP428

Subjects:
Primary: 60J80
Secondary: 60G50

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 3 • May 2009
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