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.
Citation
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
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