Sabine Jansen

Ornstein-Zernike equation in the random connection model

Connectivity properties in Gibbs measures for pointlike particles in R^d help understand phase transitions. There are several notions of connectivity in use in physics. Quantities of interest include the connectedness function and direct connectedness function, which are related by the Ornstein-Zernike equation, an integral equation that resembles the elementary renewal equation. In the physics literature it is often studied with graphical expansions in powers of the system's density (Coniglio, de Angelis, Forlani 1977). The talk addresses the convergence of the expansions in the special case where the underlying Gibbs measure is an ideal gas (Poisson point process) and explains relations with the theory of lace expansions. Based on joint work with Leonid Kolesnikov and Kilian Matzke (arXiv:2010.03826 [math-ph]).