5 papers · 1 filter
Almost sure path localisation for the derivative martingale of branching Brownian motion
Julien Berestycki, Louis Chataignier, Gabriel Flath
The evolution of the front of branching Brownian motion is determined by the limit of the derivative martingale. In this work, we characterise which particles contribute to this li…
Upper moderate deviation probabilities for the maximum of a branching random walk
Louis Chataignier, Lianghui Luo
Consider the maximal position at generation of a supercritical branching random walk. Aïdékon (2013) obtained and described the convergence in law, as time goes to in…
Upper moderate deviation probabilities for the maximum of branching Brownian motion
Louis Chataignier
It is known from Bramson (1983) that the maximum of branching Brownian motion at time is asymptotically around an explicit function , which involves a first ballistic orde…
Additive martingales of the branching Brownian motion
Louis Chataignier
In this thesis, we study asymptotic properties of the standard branching Brownian motion, with a specific emphasis on the additive martingales at high temperature. We start by pres…
Asymptotics of the overlap distribution of branching Brownian motion at high temperature
Louis Chataignier, Michel Pain
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. W…