%0 Journal Article
%T Moderate deviations for the range of a transient random walk: path concentration.
%+ Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
%+ Institut de Mathématiques de Marseille (I2M)
%A Asselah, Amine
%A Schapira, Bruno
%Z This version corrects minor mistakes from the published version.
%< avec comité de lecture
%@ 0012-9593
%J Annales Scientifiques de l'École Normale Supérieure
%I Société mathématique de France
%V 50
%N 4
%P 755--786
%8 2017
%D 2017
%K boundary of the range
%K and phrases Large deviations
%K capacity
%K range of a random walk
%K Large deviations
%Z MSC 2010 subject classifications. Primary 60F10; 60G50.
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X We study downward deviations of the boundary of the rangeof a transient walk on the Euclidean lattice. We describethe optimal strategy adopted by the walk in order toshrink the boundary of its range. The technics we developapply equally well to the range, and provide pathwise statements forthe {\it Swiss cheese} picture of Bolthausen, van den Berg andden Hollander \cite{BBH}.
%G English
%2 https://hal.science/hal-01257015v2/document
%2 https://hal.science/hal-01257015v2/file/BoundaryII-journal.corrig%C3%A9.pdf
%L hal-01257015
%U https://hal.science/hal-01257015
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ LAMA_UMR8050
%~ UPEC
%~ I2M
%~ I2M-2014-
%~ ANR
%~ UNIV-EIFFEL
%~ UPEM-UNIVEIFFEL