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Global properties of Dirichlet forms on discrete spaces

Volume 522 / 2017

Marcel Schmidt Dissertationes Mathematicae 522 (2017), 1-43 MSC: 39A70, 31C25, 60J27. DOI: 10.4064/dm738-7-2016 Published online: 7 April 2017


We provide an introduction to Dirichlet forms on discrete spaces and study their global properties including recurrence, stochastic completeness and the regularity of the Neumann form. In this setting we compare the notion of a recurrent Dirichlet form and a recurrent discrete-time Markov chain of a given graph. We prove several known and several new characterizations of recurrence by using functional-analytic Dirichlet form methods only. Finally, we compare all the above mentioned global properties and discuss their relation to spectral theory.


  • Marcel SchmidtMathematisches Institut
    Friedrich-Schiller-Universität Jena
    Ernst-Abbe-Platz 2
    07743 Jena, Germany

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