MINIMA IN BRANCHING RANDOM WALKS

• 成果类型: Article
• 署名作者: Addario-Berry, Louigi; Reed, Bruce
• 署名单位: Universite de Montreal; McGill University; Inria; Universite Cote d'Azur
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP428
• 发表日期: 2009
• 页码: 1044-1079
• 关键词: weighted height; displacement; deviations; position

摘要

Given a branching random walk, let M-n 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{vertical bar M-n - EMn vertical bar > 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.