Random Surfaces

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Random Surfaces is written by Scott Sheffield and published by . It's available with International Standard Book Number or ISBN identification 2856291872 (ISBN 10) and 9782856291870 (ISBN 13).

The author develops a general theory of discrete and continuous height models governed by Gibbs potentials that depend only on height differences. He characterizes the gradient phases of a given slope as minimizers of specific free energy and gives large deviation principles for surface shapes and empirical measures. For convex, nearest neighbor Gibbs potentials, he shows that gradient phases are characterized by their slopes and, in higher dimensional discrete settings, by one additional parameter. For standard $2+1$ dimensional crystal surface models, he shows that all smooth phases (crystal facets) lie in the dual of the lattice of translation invariance.