The Logarithmic Sobolev Constant of The Lamplighter
Evgeny Abakumov (LAMA), Anne Beaulieu (LAMA), Fran\c{c}ois Blanchard, (LAMA), Matthieu Fradelizi (LAMA), Natha\"el Gozlan (LAMA), Bernard Host, (LAMA), Thiery Jeantheau (LAMA), Magdalena Kobylanski (LAMA), Guillaume, Lecu\'e (LAMA), Miguel Martinez (LAMA), Mathieu Meyer (LAMA),
TL;DR
This paper estimates the logarithmic Sobolev constant of finite lamplighter graphs based on the spectral gap of the base graph, providing theoretical bounds and practical examples.
Contribution
It introduces bounds on the logarithmic Sobolev constant for lamplighter graphs linked to the spectral gap, with applications demonstrated.
Findings
Bounds on the logarithmic Sobolev constant derived
Relation established between spectral gap and Sobolev constant
Examples illustrating the application of theoretical results
Abstract
We give estimates on the logarithmic Sobolev constant of some finite lamplighter graphs in terms of the spectral gap of the underlying base. Also, we give examples of application.
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