Abstract
Recursion equations have been used to establish weak laws of large numbers for theminimal displacement of branching random walk in one dimension. Here, we use theseequations to establish the tightness of the corresponding sequences after appropriatecentering. These equations are special cases of recursion equations that arisenaturally in the study of random variables on tree-like structures. Such recursionequations are investigated in detail, in Bramson and Zeitouni (2006 Preprint math.PR/0612382v1), in a general context. Here, we restrict ourselvesto investigating the more concrete setting of branching random walk, and providemotivation for the rigorous arguments that are given in Bramson and Zeitouni. Wealso discuss briefly the cover time of symmetric simple random walk on regularbinary trees, which is another application of the more general recursion equations.
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