## A particle model for Wasserstein type diffusion

### With Vitalii Konarovskyi

# 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.