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Dirichlet forms and Dirichlet problems in classical and quantum probability

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If you have a question about this talk, please contact Lisa Maria Kreusser.

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Dirichlet forms have been extensively studied in classical probability theory since their introduction by A. Beurling and J. Deny in two seminal papers. In a sense, they give the repartition of the energy in a physical system and as such are related to certain partial differential equations, this connection being made by the so-called Dirichlet Problem. My goal in the first part of the talk will be to introduce them in the simple framework of a finite set and to make the connection with the associated Markov process on this set. Then we will enlarge the study to locally compact metric spaces and we will see how those ideas can be generalized to the non-commutative setting.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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