Moderate deviations for the range of a transient random walk: path concentration
Probability
2018-09-25 v3
Abstract
We study downward deviations of the boundary of the range of a transient walk on the Euclidean lattice. We describe the optimal strategy adopted by the walk in order to shrink the boundary of its range. The technics we develop apply equally well to the range, and provide pathwise statements for the {\it Swiss cheese} picture of Bolthausen, van den Berg and den Hollander \cite{BBH}.
Cite
@article{arxiv.1601.03957,
title = {Moderate deviations for the range of a transient random walk: path concentration},
author = {Amine Asselah and Bruno Schapira},
journal= {arXiv preprint arXiv:1601.03957},
year = {2018}
}
Comments
Previous version published at Annales Scientifique de l'ENS. An innocuous variance estimate is corrected