We show how to compute the spectra of several random walks that are invariant for the action of a group G in the case that the action is either not transitive or not multiplicity-free. This extends the classical analysis of stochastic processes developed by Diaconis et. al. in a Gelfand pair setting. In this expository note, we do not present the general theory, but we show the main ideas through examples, avoiding the technical results.
Examples of Markov Chains on Spaces with Multiplicities / Scarabotti, Fabio; F., Tolli. - STAMPA. - (2012), pp. 303-312. ((Intervento presentato al convegno ISCHIA GROUP THEORY 2010 tenutosi a Ischia nel 14 - 17 Aprile 2010 [10.1142/9789814350051_0024].