arXiv subjects

Daniel Boivin

Publications and source records attributed to Daniel Boivin.

3 recordsLinked to original sources

arXiv2019

Quenched large deviations for brownian motion in a random potential

A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is assumed. The proof is based on a method developed by Sznitman (1994) for Brownian motion among Poissonian potential. In particular, the LDP holds for potentials with polynomially decaying correlations such as the classical potentials studied by L. Pastur (1977) and R. Fukushima (2008) and the potentials recently introduced by H. Lacoin (2012).

math.PR↗

arXiv2012

Existence of the harmonic measure for random walks on graphs and in random environments

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on $\Z^d$, $d\geq 3$, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of $\Z^2$. This is proved using results of Barlow (2004).

math.PR↗

arXiv2006

Tail estimates for homogenization theorems in random media

It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic environments. Here we estimate the speed of convergence of this homogenization result. We obtain similar estimates for finite volume approximations of the effective conductance and of the lowest Dirichlet eigenvalue. A lower bound is also given for the variance of the Green function of a random walk in a random non-negative potential.

math.PR↗