Résumé : The rightmost particle in a branching Brownian motion at time $t$ is, with high probability, around position $2t - 3/2 \ln t$. The probability that it lies around position $c t$ with $c>2$ is exponentially small with time, with a rate which is known since Chauvin Rouault (1989). We investigate the details of these large deviations, using as a starting point an intriguing relation between the quantity we consider and the median position of the rightmost particle.

Dernière modification : Tuesday 11 February 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr