Pair interaction point processes

Link to Join MS Teams Talk

This talk will be broadcast at 15:00 BST 26th July on MS Teams only.

Meeting ID: 393 527 089 878
Passcode: dsm7py

Abstract

In statistical mechanics point processes provide a rich framework for the study of macroscopic properties of interacting microscopic entities. In the talk we formulate a convenient framework for the study of point processes which, in contrast to the Poisson process, allow for interactions between points. In particular, we focus on interactions that concern only pairs of points and are, formally, governed by a so-called pair potential. To develop some intuitive understanding of these processes, we discuss several examples from physics. On the mathematical front, we focus on the issue of rigorously defining pair interaction processes, particularly on unbounded domains, and providing guarantees for their existence. In the case of repulsive interactions, we also provide a uniqueness result - a problem related to the study of phase transitions in models of statistical mechanics. More specifically, we show that the probability distribution of a pair interaction process is uniquely determined as soon as a suitable Poisson-driven random connection model does not percolate. We relate this result to existing literature with the help of simulations and, if time permits, walk through a short sketch of the proof. (The uniqueness result is taken from a joint work with Günter Last.)

About Steffen

Steffen Betsch is a postdoc within the “Spatial Stochastics and Stochastic Geometry” group of the Institute of Stochastics at Karlsruhe Institute of Technology (KIT), where he also completed his PhD under the supervision of Günter Last.