A particle model for Wasserstein type diffusion

The discussion will be devoted to a family of interacting particles on
the real line which have a connection with the geometry of Wasserstein
space of probability measures. We will consider a physical improvement
of a classical Arratia flow, but now particles can split up and they
transfer a mass that influences their motion. The particle system can
be also interpreted as an infinite dimensional version of sticky
reflecting dynamics on a simplicial complex. The model appears as a
martingale solution to an infinite dimensional SDE with discontinuous
coefficients. In the talk, we are going to consider a reversible case,
where the construction is based on a new family of measures on the set
of real non-decreasing functions as reference measures for naturally
associated Dirichlet forms. In this case, the intrinsic metric leads
to a Varadhan formula for the short time asymptotics with the
Wasserstein metric for the associated measure valued diffusion. The
talk is based on joint work with Max von Renesse.

• Speaker: Vitalii Konarovskyi
• Tuesday 22 May 2018, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.