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arXiv · 1601.03957

Moderate deviations for the range of a transient random walk: path concentration

Amine Asselah·Bruno Schapira
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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}.

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Amine Asselah, Bruno Schapira. 2016-01-15. Moderate deviations for the range of a transient random walk: path concentration. https://arxiv.org/abs/1601.03957

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