Leonardo Rolla (DMA, ENS Paris)

A review of graphical methods for interacting particle and spin systems with applications

vendredi 4 juin 2010, 13h30 - 15h30

Salle de réunion, espace Turing


In this talk we will present a review of graphical constructions used
in the study of several random spatial processes, most notably spin
and interacting particle systems.

We start with the celebrated Poisson-point construction mostly
attributed to T. E. Harris, the so-called « basic coupling ». We then
introduce the distributed-processor construction due to Diaconis,
Fulton, and Eriksson, where the system is approached as sequence of
well-behaved operations rather than a continuous-time evolution.

Applications of Harris type of construction percolate the literature
of exclusion processes, voter model, contact procecess, coalescing
random walks, Ising model, to mention a few. On the other hand,
Diaconis-Fulton-Eriksson type of construction proves invaluable in
the study of internal DLA, sandpiles, set smash sum, Wilson’s
algorithm for uniform spanning trees, reaction-diffusion models,…

Besides the forementioned applications, we will explain a joint work
with V. Sidoravicius, where we estabilish an absorbing-state phase
transition for activated random walks and stochastic sandpiles.