Condensed Matter Seminar: Phase transitions in dense random graphs

Prof. Lorenzo Sadun, University of Texas, Austin

19 March 2018, 11:00 
Kaplun Building, Flekser Hall 118 
Condensed Matter Seminar

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

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