Laws of the iterated logarithm for the range of random walks in two and three dimensions

DOI10.1214/aop/1029867131zbMath1031.60031OpenAlexW2011604975MaRDI QIDQ1872297

Richard F. Bass, Takashi Kumagai

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1029867131

zbMATH Keywords

law of the iterated logarithmintersection local timerange of random walkalmost sure invariance principle

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Sample path properties (60G17)

Related Items (15)

Range-renewal processes: SLLNs and power laws ⋮ Moderate and small deviations for the ranges of one-dimensional random walks ⋮ On the range of pinned random walks ⋮ Large deviations of the range of the planar random walk on the scale of the mean ⋮ Strong approximations of three-dimensional Wiener sausages ⋮ Asymptotic entropy of the ranges of random walks on discrete groups ⋮ Invariance principle for the capacity and the cardinality of the range of stable random walks ⋮ Capacity of the range of random walks on groups ⋮ Self-intersection local time: critical exponent, large deviations, and laws of the iterated logarithm ⋮ Functional CLT for the range of stable random walks ⋮ Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks ⋮ Some results for range of random walk on graph with spectral dimension two ⋮ Limit theorems for a stable sausage ⋮ Unnamed Item ⋮ An almost sure invariance principle for the range of planar random walks

Cites Work

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• The range of stable random walks
• Propriétés d'intersection des marches aléatoires. I: Convergence vers le temps local d'intersection. (Properties of intersection of random walks. I: Convergence to local time intersection)
• Fluctuation results for the Wiener sausage
• Local times on curves and uniform invariance principles
• Further limit theorems for the range of random walk
• The fluctuation result for the multiple point range of two dimensional recurrent random walks
• Laws of the iterated logarithm for some symmetric diffusion processes
• Large deviations for the range of an integer valued random walk
• An almost sure invariance principle for the range of random walks
• The range of transient random walk
• Probability Inequalities for the Sum of Independent Random Variables
• On the number of distinct sites visited by a random walk
• Foundations of Modern Probability
• The range of recurrent random walk in the plane
• The Law of the Iterated Logarithm for the Range of Random Walk
• A large-deviation result for the range of random walk and for the Wiener sausage

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