Calendar of Seminars & Colloquia

This calendar is updated on an ongoing basis. If you would like to include a talk to this calendar, please send your announcement to Rose Choi at rosechoi[at]math.washington.edu. Be sure to include a link to the seminar webpage where the abstract is posted and render any LaTeX when applicable.

Week of July 7 - 11
Monday
 
Tuesday
 
Wednesday
 
Thursday

Probability Seminar
Rigidity in Markovian Maximal couplings w/ Sayan Banerjee

Coupling is a way of embedding two Markov processes with given marginal laws in a common probability space, building in useful dependencies in the joint law. A maximal coupling is a coupling where the Markov processes meet the fastest, and a Markovian maximal coupling (MMC) is a maximal coupling where the individual processes are not allowed to cheat by looking into the future (for example, if both processes are Markov with respect to a common filtration). Although maximal couplings have been shown to exist by Griffeath ('75) and Pitman ('76), the description is quite complicated and involves a path decomposition where we look into the future. A natural question that arises is: when does a MMC exist? An answer to this question would lead to simpler descriptions and better understanding of couplings.

We show, confirming popular folklore and remarks in earlier papers, that for diffusions, the presence of a MMC imposes a rigidity on the coupling, forcing the drift to be of a particularly simple form. This is reminiscent of some classic results in geometry where the presence of some geometric property imposes enough rigidity for the manifold to be completely characterised.

SAV 131, 2:30pm

Friday
 

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