Random Surfaces

Random surfaces, or random height functions, are random functions defined on Z d or Rd and taking values (heights) in Z or R. Their distributions are determined by Gibbs potentials invariant under a lattice of translations and depending only on height differences. This is a general framework that covers many particular models considered in the literature. In this setting, a variational principle is proved, namely invariant Gibbs measures of given slope are those of minimal specific free energy. Continuous models are approximated by discrete ones with increasing resolution and a large deviation principle is proved. New results concerning the uniqueness of the Gibbs state are presented. The book concludes with a list of open problems.

Reviewer: 
jrat
Book details
Author:  Publisher: 
Published: 
2005
ISBN: 
978-2-85629-186-3
Price: 
EUR 26
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