Condensed Matter Seminar: Phase transitions in dense random graphs

Abstract:

We consider large dense random graphs with constraints on the density of various features. For instance, we might consider graphs where 60% of the possible edges are present, and where 21.5% of the triples of vertices form triangles. The ensemble of such graphs, analogous to the microcanonical ensemble of statistical mechanics, is described by a "graphon" that maximizes a certain entropy functional. This graphon varies smoothly with the parameters in a region, and but changes form at certain phase transition lines. In this talk I'll describe the phase structure of the edge-triangle model, and exhibit analogues to both first- and second-order phase transitions. This is joint work with Rick Kenyon, Charles Radin and Kui Ren.

Event Organizer: Prof. Alexander Gerber