The Logarithmic Sobolev Constant of The Lamplighter

Evgeny Abakumov, Anne Beaulieu, François Blanchard, Matthieu Fradelizi, Nathaël Gozlan, Bernard Host, Thiery Jeantheau, Magdalena Kobylanski, Guillaume Lecué, Miguel Martinez, Mathieu Meyer, Marie-Hélène Mourgues, Frédéric Portal, Francis Ribaud, Cyril Roberto, Pascal Romon, Julien Roth, Paul-Marie Samson, Pierre Vandekerkhove, Abdellah Youssfi

Published 2010-11-08Version 1

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.