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Computing Norms of Group-Invariant Transition Operators

Published online by Cambridge University Press:  12 September 2008

Laurent Saloff-Coste  and
Wolfgang Woess
Laurent Saloff-Coste
Affiliation:
CNRS, Statistique et Probabilités, Université Paul Sabatier, 31062 Toulouse Cedex, France
Wolfgang Woess
Affiliation:
Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy
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Abstract

We consider transition operators P on a countable set, which are reversible, irreducible and invariant under a group G of permutations of X with compact point stabilizers. We relate the computation of the spectral radius (norm) of P with the spectral radii of certain matrices defined over the factor set G\X. In various cases, this allows easy computation of the norm of P.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 2 , June 1996 , pp. 161 - 178
Copyright
Copyright © Cambridge University Press 1996

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