On large deviations for the cover time of two-dimensional torus

Let Tn be the cover time of two-dimensional discrete torus Z2 n = Z2=nZ2. We prove that P[Tn 4 n2 ln2 n] = exp(n2(1 p )+o(1)) for 2 (0; 1). One of the main methods used in the proofs is the decou- pling of the walker's trace into independent excursions by means of soft local times.

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Source https://hal.science/hal-00838261
Author Comets, Francis, Gallesco, Christophe, Popov, Serguei, Vachkovskaia, Marina
Maintainer CCSD
Last Updated May 10, 2026, 14:04 (UTC)
Created May 10, 2026, 14:04 (UTC)
Identifier hal-00838261
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de Probabilités et Modèles Aléatoires (LPMA) ; Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
creator Comets, Francis
date 2013-06-14T00:00:00
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harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-09-29T00:00:00
set_spec type:UNDEFINED