abstract:
In this lecture we will discuss diffusions in random environment and in particular a recent result obtained jointly with Ofer Zeitouni proving a functional central limit theorem for isotropic diffusions in random environment that are small perturbations of Brownian motion when the space dimension is three or higher.
additional material:
slides of first lecture (Feb 10)
abstract:
In statistical mechanics, partition
functions play an important role in encoding the statistical properties of a
system in thermodynamic equilibrium.
The functions can be described as the total interaction of states that the
vertices of a graph can adopt, for a given probability distribution of
states and a given valuation of the interaction of pairs of states.
With M. Freedman and L. Lovasz, we characterized partition functions among
all graph parameters.
The characterization is in terms of `reflection positivity', and the proof
is based on commutative algebra.
In the talk we will explain this theorem and discuss some further results.