Capacity of the range of random walk on \(\mathbb{Z}^{4}\)

DOI10.1214/18-AOP1288zbMath1467.60017arXiv1611.04567OpenAlexW2963285875MaRDI QIDQ2421820

Amine Asselah, Bruno Schapira, Perla Sousi

Publication date: 18 June 2019

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

Full work available at URL: https://arxiv.org/abs/1611.04567

zbMATH Keywords

capacitylaw of large numberscentral limit theoremGreen kernel

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (14)

Statistical properties of sites visited by independent random walks ⋮ Percolation of worms ⋮ Capacity of the range of tree-indexed random walk ⋮ Central limit theorem for the capacity of the range of stable random walks ⋮ Large deviations of the range of the planar random walk on the scale of the mean ⋮ Asymptotic capacity of the range of random walks on free products of graphs ⋮ Convergence in law for the capacity of the range of a critical branching random walk ⋮ Logarithmic corrections to scaling in the four-dimensional uniform spanning tree ⋮ Invariance principle for the capacity and the cardinality of the range of stable random walks ⋮ Capacity of the range of random walks on groups ⋮ Capacity of the range in dimension 5 ⋮ The boundary of the range of a random walk and the Følner property ⋮ Functional CLT for the range of stable random walks ⋮ Deviations for the capacity of the range of a random walk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase transition in loop percolation
• The self-avoiding walk.
• The range of stable random walks
• Vacant set of random interlacements and percolation
• The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory
• Intersection properties of simple random walks: A renormalization group approach
• Intersections of random walks in four dimensions. II
• 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
• A self-avoiding random walk
• The probability of intersection of independent random walks in four dimensions
• Intersections of Brownian motions
• Strong law of large numbers for the capacity of the Wiener sausage in dimension four
• Torsional rigidity for regions with a Brownian boundary
• Intersections of random walks and Wiener sausages in four dimensions
• The trace of spatial Brownian motion is capacity-equivalent to the unit square
• Non-intersection exponents for Brownian paths. Part I: Existence and an invariance principle
• On the volume of the intersection of two Wiener sausages
• On the range of random walk
• The range of transient random walk
• Two observations on the capacity of the range of simple random walks on \(\mathbb{Z} ^3\) and \(\mathbb{Z} ^4\)
• Connectivity properties of random interlacement and intersection of random walks
• Random Walk: A Modern Introduction
• Random Walks and Quantum Gravity in Two Dimensions
• Capacity of the range of random walk on $\mathbb {Z}^d$
• Moderate deviations for the range of a transient random walk: path concentration
• Asymptotics of the critical time in Wiener sausage percolation with a small radius
• Probability
• Values of Brownian intersection exponents. II: Plane exponents

This page was built for publication: Capacity of the range of random walk on \(\mathbb{Z}^{4}\)