Self-intersection local time: critical exponent, large deviations, and laws of the iterated logarithm

DOI10.1214/009117904000000504zbMath1075.60097arXivmath/0503592OpenAlexW1965749763MaRDI QIDQ1769512

Richard F. Bass, Xia Chen

Publication date: 21 March 2005

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503592

zbMATH Keywords

Brownian motion

Mathematics Subject Classification ID

Large deviations (60F10) Local time and additive functionals (60J55)

Related Items (19)

Random walk in random scenery and self-intersection local times in dimensions \(d \geq 5\) ⋮ Moderate deviations and laws of the iterated logarithm for the local times of additive Lévy processes and additive random walks ⋮ Large deviations and laws of the iterated logarithm for the local times of additive stable processes ⋮ Large deviations in total variation of occupation measures of one-dimensional diffusions ⋮ Moderate and small deviations for the ranges of one-dimensional random walks ⋮ Existence and smoothness of local time and self-intersection local time for spherical Gaussian random fields ⋮ Self-intersection local times of random walks: exponential moments in subcritical dimensions ⋮ Stochastic heat equation driven by fractional noise and local time ⋮ Large deviations estimates for self-intersection local times for simple random walk in \({\mathbb{Z}}^3\) ⋮ Large deviations for intersection local times in critical dimension ⋮ Remarks on the intersection local time of fractional Brownian motions ⋮ Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks ⋮ Large deviations for renormalized self-intersection local times of stable processes ⋮ Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks ⋮ Self-intersection local times of additive processes: large deviation and law of the iterated logarithm ⋮ Integral representation of renormalized self-intersection local times ⋮ Renormalized self-intersection local time of bifractional Brownian motion ⋮ Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise ⋮ An almost sure invariance principle for the range of planar random walks

Cites Work

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• Nonlinear Schrödinger equations and sharp interpolation estimates
• Self-intersections of random fields
• Regularized self-intersection local times of planar Brownian motion
• Local times on curves and uniform invariance principles
• Intersection local times and Tanaka formulas
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• Large and moderate deviations for intersection local times
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Tanaka's formula and renormalization for intersections of planar Brownian motion
• Laws of the iterated logarithm for the range of random walks in two and three dimensions
• Brownian intersection local times: Upper tail asymptotics and thick points
• Chaos expansions of double intersection local time of Brownian motion in \(\mathbb{R}^ d\) and renormalization
• Exponential asymptotics for intersection local times of stable processes and random walks

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