Sém. Proba. L. Miclo. Construction of set-valued dual processes via random mappings

schedule du mardi 20 novembre 2018 à 14h00 au jeudi 20 décembre 2018 à 15h00

Organisé par : LPSM

Intervenant : Laurent MICLO (U. P. Sabatier.)
Lieu : Campus Jussieu, Tours-16-26, 2ème, Salle 209.

Sujet : L. Miclo: Construction of set-valued dual processes via random mappings

Résumé :

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.