23-33 Charles Radin, Lorenzo Sadun

OPTIMAL GRAPHONS IN THE EDGE-2STAR MODEL (481K, pdflatex) May 2, 23

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. In the edge-2star model with hard constraints we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optimal graphons related by a symmetry. At each point in the open set but off the line segment there is a unique entropy-optimizer, bipodal and varying analytically with the constraints. We also show that throughout another open set, containing a different portion of the same line of symmetry, there is instead a unique optimal graphon, varying analytically with the parameters. We explore the extent of these open sets, determining the point at which a symmetric graphon ceases to be a local maximizer of the entropy. Finally, we prove some foundational theorems in a general setting, relating optimal graphons to the Boltzmann entropy and the generic structure of large constrained random graphs.

Files: 23-33.src( 23-33.keywords , 2star14.pdf.mm )