abstract:
The Internal Diffusion
Limited Aggregation (IDLA) is a random growth model introduced by
Diaconis and Fulton in 1991. Particles are produced by an internal fixed
source and are trapped at their first visit to a site never visited by a
former particle. The cloud of trapped particles is then growing.
We will present this model on the grid Z^d and discuss the different
versions (rate of production of the particles / law of the diffusion)
and related results about the asymptotic shape of the cloud of trapped
particles.
Then we will focus on IDLA on graphs with exponential volume growth
(e.g. trees) where the limiting shape can be described using a new
metric called the Green metric (which happens to have some nice
geometric properties that will be discussed aside).
We will also give a more precise description of that shape in the case
of homogeneous trees.
(Joint work with Sara
Brofferio.)
abstract:
We will discuss Gaussian and
non-Gaussian deviation bounds in the context of Gibbsian random fields. The
link with the relaxational behavior of the reversible Glauber or Kawasaki
dynamics will be discussed.
We will also discuss the link with the log-Sobolev, the Poincare inequality
and so-called transportation cost inequalities.
The research on which this talk is based is joint work with J.R. Chazottes,
P. Collet and C. Külske.
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