The distribution function of the rightmost particle in a branching Brownian

motion satisfies the Fisher-KPP equation:

∂u/∂t = ∂²u/∂x² + u – u²

Such an equation appears also in biology, chemistry or theoretical physics

to describe a moving interface, or a front, between a stable and an unstable

medium.

Thirty years ago, Bramson gave rigorous sharp estimates on the position of

the front, and, fifteen years ago, Ebert and van Saarloos heuristically

identified universal vanishing corrections.

In this presentation, I will present a novel way to study the position of

such a front, which allows to recover all the known terms and find some new

ones. We start by studying a front equation where the non-linearity is

replaced by a condition at a free boundary, and we show how to extend our

results to the actual Fisher-KPP.

**Date**: 29 April 2019, 12:00 (Monday, 1st week, Trinity 2019)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Speaker**: Éric Brunet (Laboratoire de Physique Statistique, ENS Paris)**Organising department**: Department of Statistics**Organisers**: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt