Asymptotics of the overlap distribution of branching Brownian motion at high temperature

At high temperature, the overlap of two particles chosen independently according to the Gibbs measure of the branching Brownian motion converges to zero as time goes to infinity. We investigate the precise decay rate of the probability to obtain an overlap greater than $a$, for some $a>0$, in the whole subcritical phase of inverse temperatures $β\in [0,β_c)$. Moreover, we study this probability both conditionally on the branching Brownian motion and non-conditionally. Two sub-phases of inverse temperatures appear, but surprisingly the threshold is not the same in both cases.

💡 Research Summary

This paper, “Asymptotics of the overlap distribution of branching Brownian motion at high temperature,” provides a detailed analysis of the precise decay rates for the probability that the overlap between two particles chosen independently from the Gibbs measure of a Branching Brownian Motion (BBM) exceeds a fixed threshold a > 0. The study focuses exclusively on the high-temperature (subcritical) phase where the inverse temperature β lies in