Student Probability Seminar

2D Gibbsian Point Processes: Preservation and Breaking of Symmetries for the Hard Core Potential

Speaker: Alexisz Gaal

Location: Warren Weaver Hall 1314

Date: Thursday, October 22, 2015, 2 p.m.


A mathematically rigorous model of crystallization using the Gibbs distribution haven't been constructed yet. The phase transitions of freezing and melting seem out of reach for mathematicians. We will look at a Poisson point process in a bounded sets of \(\mathbb{R}^2\) with constant intensity \(z>0\) conditioned on the event that two Poisson points have distance greater than 1. I will quote a result to extend this process to the whole plane and we will look at properties of such extensions. Existence (for large class of such processes) and translational invariance were shown in 2011 and 2008. Breaking of the rotational symmetry is indicated in a few toy models. My goal is to discuss one of these toy models. Breaking of the rotational symmetry is believed to model the phase transition from liquid to solid crystal.