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

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.

References in corpus (2)

• Minimal supporting subtrees for the free energy of polymers on disordered trees
• The critical random barrier for the survival of branching random walk with absorption

Cited by in corpus (2)

• The slow regime of randomly biased walks on trees
• Range and critical generations of a random walk on Galton-Watson trees