The One World Probability Seminar is back!

This Semester it will take place every other Wednesday form 15:00 to 17:00 UTC. You can find more information on the web site:

https://www.owprobability.org/one-world-probability-seminar.

OWPS's next session will be on Wednesday the 15th of February from 15:00 to 17:00 UTC. Our next speakers are:

Frank den Hollander (Leiden) and Elena Pulvirenti (Delft)

Title, abstract and the zoom link are below the signature and can be found on the website https://www.owprobability.org/one-world-probability-seminar.

Best wishes, Alberto Chiarini (Padua) and Adrián González Casanova (Berkeley and México)

-----------------------------------------------------------------------------------------------------------

Speakers: Frank den Hollander (Leiden) and Elena Pulvirenti (Delft)

Talk 1 : Metastability for the Widom-Rowlinson model: I. Planar discs.

Abstract

We define the static Widom-Rowlinson model on a two-dimensional finite torus. The energy of a particle configuration is determined by its halo, defined as the union of unit discs centred at the positions of the particles. We discuss the metastable behaviour of a dynamic version of the model, in which particles are randomly created and annihilated as if the outside of the torus were an infinite reservoir with a given chemical potential. We start with the empty torus and are interested in the first time when the torus is fully covered by unit discs. This can be viewed as the crossover time from a ‘gas phase’ to a ‘liquid phase’. We consider the metastable regime where the temperature is low and the chemical potential is supercritical. In order to achieve the transition from empty to full, the system needs to create a sufficiently large droplet, called critical droplet, which triggers the crossover. It turns out that the critical droplet is close to a disc of a certain deterministic radius, with a boundary that is random and consists of a large number of unit discs that stick out by a small distance. We show how an analysis of the surface fluctuations allows us to derive both a volume term and a surface term in the asymptotics of the average crossover time.

Based on joint work with Sabine Jansen (Munich) and Roman Kotecký (Prague).

Talk 2 : Metastability for the Widom-Rowlinson model: II. Grains of general shape.

Abstract

We investigate what happens when the planar discs are replaced by convex grains in arbitrary dimensions whose shape may be random. We identify the size and the shape of the critical droplet as a function of the shape distribution for the grains. We also identify the volume term in the asymptotics of the average crossover time. In addition, we speculate about the surface term, formulating a conjecture about what it should look like. There are various interesting subcases, showing that the shape of the grains has a rather delicate influence on the critical droplet and the average crossover time.

Based on joint work with Yogesh Dhandapani (Bangalore) and Roman Kotecký (Prague).

Zoom-link: https://unipd.zoom.us/j/89537602090?pwd=T0lETjRKaHk1R3FpWmNTbThxNTJQdz09 Meeting ID: 895 3760 2090 Passcode: 300934

If you are having trouble with zoom, or if the capacity of the zoom room gets exceeded, you can also access to the Youtube live stream at the channel of the seminar: https://www.youtube.com/channel/UCiLiEQGTp6bZEhuHDM-WNWQ