First order transition for the branching random walk at the critical parameter

Thomas Madaule

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arXiv · 1206.3835

First order transition for the branching random walk at the critical parameter

Thomas Madaule

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Abstract

Considering a critical branching random walk on the real line. From a study of the law of the trajectory of a particle chosen under the polymer measure, we establish a first order transition for the partition function at the critical parameter. This result is strongly related to a recent paper of Aïdékon and Shi in which they solved the problem of the normalisation of the partition function in the critical regime.

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Thomas Madaule. 2013-08-06. First order transition for the branching random walk at the critical parameter. https://arxiv.org/abs/1206.3835

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