Capacity of the range of random walks on groups
Rudi Mrazovi\'c, Nikola Sandri\'c, Stjepan \v{S}ebek
TL;DR
This paper investigates the asymptotic properties of the capacity of the range of symmetric simple random walks on finitely generated groups, establishing a strong law of large numbers and a central limit theorem.
Contribution
It introduces new asymptotic results, including a strong law and a CLT, for the capacity of the range of random walks on groups.
Findings
Proves a strong law of large numbers for capacity
Establishes a central limit theorem for capacity
Provides asymptotic behavior analysis of the capacity
Abstract
In this paper, we discuss asymptotic behavior of the capacity of the range of symmetric simple random walks on finitely generated groups. We show the corresponding strong law of large numbers and central limit theorem.
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Taxonomy
TopicsGeometric and Algebraic Topology · Limits and Structures in Graph Theory · advanced mathematical theories