Asymptotic characteristics of Markov operators on groupoids

Lundi 28 février 2011 14:00-15:00 - Kaimanovich Vadim - Univ. Ottawa

Résumé : It is well-known that inherent homogeneity makes analysis on groups much more interesting than on general graphs or manifolds. However, there are numerous situations when the considered operators (and the underlying spaces), although not homogeneous sensu stricto, still have properties similar to invariant operators on groups. Numerous examples are provided by covering manifolds and graphs, foliations, laminations and graphed equivalence relations, or, from probabilistic point of view, by various models of random walks in random environment, with internal degrees of freedom, etc.
We shall introduce the notion of an invariant Markov operator on a groupoid and show how all the above situations can be interpereted in these terms. Further we shall discuss the Liouville property for harmonic functions on groupoids and its links with qualitatitave (amenability) and quantitative (entropy, rate of escape) characteristics of groupoids and Markov operators on them.

Lieu : bât. 425 - 113-115

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