Lamplighter random walks on fractals
Takashi Kumagai, Chikara Nakamura
TL;DR
This paper investigates the behavior of lamplighter random walks on fractal graphs, focusing on heat kernel estimates and laws of the iterated logarithms, assuming the underlying graph exhibits sub-Gaussian heat kernel behavior.
Contribution
It provides new on-diagonal heat kernel estimates and laws of the iterated logarithms for lamplighter walks on fractals under sub-Gaussian conditions.
Findings
Established on-diagonal heat kernel estimates for lamplighter walks.
Derived laws of the iterated logarithm for these walks.
Extended results to fractal graphs with sub-Gaussian heat kernel estimates.
Abstract
We consider on-diagonal heat kernel estimates and the laws of the iterated logarithms for a switch-walk-switch random walk on a lamplighter graph under the condition that the random walk on the underlying graph enjoys sub-Gaussian heat kernel estimates.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · advanced mathematical theories