236 research outputs found
Minima in branching random walks
Given a branching random walk, let be the minimum position of any
member of the th generation. We calculate to within O(1) and
prove exponential tail bounds for , 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 when the branching
random walk has bounded branching and step size.Comment: Published in at http://dx.doi.org/10.1214/08-AOP428 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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