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

Francis Comets (1) , Christophe Gallesco (2) , Serguei Popov (2) , Marina Vachkovskaia (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IMECC - Instituto de Matemática, Estatística e Computação Científica [Brésil]

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.

Mots clés: soft local time; hitting time; simple random walk; cover time

Domaines: Probabilités [math.PR]

Francis Comets, Christophe Gallesco, Serguei Popov, Marina Vachkovskaia. On large deviations for the cover time of two-dimensional torus. 2013. ⟨hal-00838261⟩