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