Jean-Christophe Mourrat (EPFL)
Title: Quantitative homogenization of random environments
we observe a random walk moving among random i.i.d. conductances on
larger and larger diffusive scales, it is known that we obtain a
Brownian motion with a constant covariance matrix in the limit. I will
describe recent progress on the question of quantifying this
convergence. From the PDE's perspective, one considers instead the
(divergence form) generator of the random walk, and similarly if one
looks at this operator from a distance, it tends to look like an
operator with constant "homogenized" coefficients. An important
question in numerical analysis is to be able to compute these
coefficients. We will see how the analysis of certain techniques of
estimation of these coefficients can be linked with the probabilistic
- Variance decay for functionals of the environment viewed by the particle, Ann. Inst. Henri Poincaré Probab. Stat. 47 (1), 294-327 (2011).
- Other refences here.