Probability Seminar: Stefan Adams
Topic
Phase Transitions in Continuum Delaunay Potts Models
Speakers
Details
We discuss recent results on phase transitions of Delaunay Potts models in dimension two where the interaction depends on Delaunay edges respectively Delaunay triangles.
This work is an extension of the Lebowitz & Lieb soft-core continuum Potts model to geometrically dependent interaction systems. The main tool is a FK (Fortuin-Kasteleyn) random cluster representation adapted to the Delaunay structure and percolation in the FK model. If time permits we discuss the Voronoi-Ising model where the interaction is function of the length of the common boundary and its connection to variants of the RSW (Russo-Seymour-Welsh) theorem in continuum percolation.
This work is an extension of the Lebowitz & Lieb soft-core continuum Potts model to geometrically dependent interaction systems. The main tool is a FK (Fortuin-Kasteleyn) random cluster representation adapted to the Delaunay structure and percolation in the FK model. If time permits we discuss the Voronoi-Ising model where the interaction is function of the length of the common boundary and its connection to variants of the RSW (Russo-Seymour-Welsh) theorem in continuum percolation.
Additional Information
Location: ESB 2012
Stefan Adams, Warwick University
Stefan Adams, Warwick University