Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75541Let B_n be the number of self-intersections of a symmetric random walk with finite second moments in the integer planar lattice. We obtain moderate deviation estimates for B_n - E B_n and E B_n- B_n, which are given in terms of the best constant of a certain Gagliardo-Nirenberg inequality. We also prove the corresponding laws of the iterated logarithm.Probability60J55Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walkstext