Amine Asselah, Bruno Schapira
Published 2016-01-15Version 1
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}.
Large deviations of the range of the planar random walk on the scale of the mean
Large deviations for the local times of a random walk among random conductances
On the nature of the Swiss cheese in dimension 3
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