Construction of set-valued dual processes via random mappings – Laurent Miclo

Laurent Miclo
IMT, Université Paul Sabatier Toulouse III
https://perso.math.univ-toulouse.fr/miclo/

Date(s) : 30/11/2018   iCal
11 h 00 min - 12 h 00 min

The strong stationary times introduced by Aldous and Diaconis [1986] provide a probabilistic approach to quantitative convergence to equilibrium.
They are often obtained as the absorption times of intertwining dual processes, following a method due to Diaconis and Fill [1990].
We will see how to deduce explicit constructions from certain random mappings, related to the coupling-from-the-past algorithm of Propp and Wilson [1996] and to the evolving sets of Morris and Peres [2005]. This approach is very flexible and can be adapted, via the coalescing stochastic flows of Le Jan and Raimond [2006] associated to Tanaka’s equation, to recover Pitman’s theorem [1975] on the intertwining relation between the Brownian motion and the Bessel-3 process. The talk will end by the presentation of a new kind of coalescing stochastic flows that would enable us to go further.

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