Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
Abstract
Let Bn 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 Bn - E Bn and E Bn- Bn, 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.