Singularities in Gaussian Random Fields
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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This paper discusses a Gaussian random field that arises in pattern analysis. This random field exhibits phase transitive behavior for a particular value of the temperature parameter. We analyze this kind of non singular behavior and the effect that it has on the field random variables. The limiting specific heat also exhibits a phase transition with a power law behavior. One of the principal aims of statistical mechanics is to derive the thermodynamic behavior of macroscopic bodies beginning from a description of their microscopic components. A good deal of work has been done on modelling ferromagnetic and antiferromagnetic behavior. A magnet can be considered to have a large number of magnetic domains, to each of which a magnetic spin is associated that represents the direction of magnetization at that domain. We usually assume that the spins take two values, 0 and 1. The physical models usually postulate that these domains are sites or vertices in a graph.
- Statistics and Probability