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

F. Comets (1) , C. Gallesco , S. Popov , M. Vachkovskaia

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Let T-n be the cover time of two-dimensional discrete torus Z(n)(2) = Z(2)/nZ(2). We prove that P[T-n <= 4/pi gamma n(2) ln(2) n] = exp(-n(2(1-root gamma)+o(1))) for gamma is an element of (0, 1). One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times

Domaines: Probabilités [math.PR]

F. Comets, C. Gallesco, S. Popov, M. Vachkovskaia. On large deviations for the cover time of two-dimensional torus. Electronic Journal of Probability, 2013, 18 (96), pp.1-18. ⟨10.1214/EJP.v18-2856⟩. ⟨hal-01017852⟩