Orateur
M.
Jean-François Le Gall
Description
Brownian motion indexed by the Brownian tree appears in the
asymptotics of many models of combinatorics or statistical physics,
and is also closely related to super-Brownian motion. We
consider the process of local times of (one-dimensional) Brownian motion
indexed by the Brownian tree and we show that, although this
process is not Markov, the pair formed by the local time and
its derivative is a Markov process. In a work in collaboration with
Ed Perkins, we prove that this pair satisfies a stochastic
differential equation whose drift involves the classical Airy function.
This is an analog of the well-known Ray-Knight theorems
for linear Brownian motion.
