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Journal Articles Annals of Probability Year : 2009

Minima in branching random walks


Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\\mathbfEM_n$ to within O(1) and prove exponential tail bounds for $\\mathbfP{|M_n-\\mathbfEM_n|>x}$, 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 $\\mathbf EM_n$ when the branching random walk has bounded branching and step size.
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hal-00795281 , version 1 (27-02-2013)


  • HAL Id : hal-00795281 , version 1


Louigi Addario-Berry, Bruce Reed. Minima in branching random walks. Annals of Probability, 2009, 37, pp.1044―1079. ⟨hal-00795281⟩
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