Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks

2005/05/01 by Xia Chen · 3 citations
Mathematics · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.PR #msc:60D05 #msc:60F10 #msc:60F15 #msc:60G50

paper · pdf · doi:10.1214/009117905000000035

published as Annals of Probability 2005, Vol. 33, No. 3, 1014-1059 · Published at http://dx.doi.org/10.1214/009117905000000035 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/05/01 · arxiv created 2005/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S₁(n),…,S_p(n) be independent symmetric random walks in \mathbb Z^d. We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #\S₁[0,n]∩⋯∩S_p[0,n]\ in the case d=2, p≥2 and the case d=3, p=2.

Citations

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
• Nonlinear Schr�dinger equations and sharp interpolation estimates
• Large deviations for renormalized self-intersection local times of stable processes

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