Alberto Chiarini

Quenched invariance principle for random walks with time-dependent ergodic degenerate weights

We study a continuous-time random walk, XX, on ZdZd in an environment of dynamic random conductances taking values in (0,∞)(0,∞). We assume that the law of the conductances is ergodic with respect to space–time shifts. We prove a quenched invariance principle for the Markov process XX under some moment conditions on the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.

Invariance principle for symmetric diffusions in a degenerate and unbounded stationary and ergodic random medium

We study a symmetric diffusion

Extremes of Some Gaussian Random Interfaces

X

A note on the extremal process of the supercritical Gaussian Free Field

on

Extremes of the supercritical Gaussian Free Field

\mathbb{R}^d

Local central limit theorem for diffusions in a degenerate and unbounded random medium

in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients

Approximating conditional distributions

a^\omega

A note on the Green's function for the transient random walk without killing on the half lattice, orthant and strip

. The diffusion is formally associated with

Entropic repulsion for the Gaussian free field conditioned on disconnection by level-sets.

L^\omega u = \nabla\cdot(a^\omega\nabla u)

Extremes of some Gaussian random interfaces

, and we make sense of it through Dirichlet forms theory. We prove for