Geometric homogeneity in disordered spatial processes
- Series
- Job Candidate Talk
- Time
- Tuesday, December 2, 2014 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Eviatar Procaccia – University of California, Los Angeles
Experimentalists observed that microscopically disordered systems exhibit
homogeneous geometry on a macroscopic scale. In the last decades elegant
tools were created to mathematically assert such phenomenon. The classical
geometric results, such as asymptotic graph distance and isoperimetry of
large sets, are restricted to i.i.d. Bernoulli percolation. There are many
interesting models in statistical physics and probability theory, that
exhibit long range correlation.
In this talk I will survey the theory, and discuss a new result proving,
for a general class of correlated percolation models, that a random walk on
almost every configuration, scales diffusively to Brownian motion with
non-degenerate diffusion matrix. As a corollary we obtain new results for
the Gaussian free field, Random Interlacements and the vacant set of Random
Interlacements. In the heart of the proof is a new isoperimetry result for
correlated models.