We present an introduction to the theory of Finite Gelfand Pairs and to their application to the study of the asymptotic behaviour of some Markov chains (the Bernoulli-Laplace diffusion model). We shall also present some new examples arising from Geometric Group Theory (self-similar groups, branch groups, the Basilica group, iterated monodromy groups) and the Theory of Association Schemes (generalized wreath products of permutation groups).
Finite Gelfand pairs: examples and applications / Scarabotti, Fabio; CECCHERINI SILBERSTEIN, T; D'Angeli, D; Donno, Alfredo; Tolli, F.. - STAMPA. - (2009), pp. 7-41. ((Intervento presentato al convegno Ischia group theory 2008. tenutosi a Ischia nel 1-4 Aprile 2008.