Gibbs states on random configurations

Comment: On Random Scan Gibbs Samplers

We congratulate the authors on a review of convergence rates for Gibbs sampling routines. Their combined work on studying convergence rates via orthogonal polynomials in the present paper under discussion (which we will denote as DKSC from here onward), via coupling in Diaconis, Khare and SaloffCoste (2006), and for multivariate samplers in Khare and Zhou (2008), enhances the toolbox of theoret...

One-Dimensional Random-Field Ising Model: Gibbs States and Structure of Ground States

We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibbs state is unique for any realization of the external field. Then we prove that as T-* 0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the externa...

On Two-point Configurations in Random Set

We show that with high probability a random set of size Θ(n1−1/k) of {1, . . . , n} contains two elements a and a+ dk, where d is a positive integer. As a consequence, we prove an analogue of Sárközy-Fürstenberg’s theorem for random set.

Random walks, random configurations, and horocyclic products

On a Parameter Estimation Method for Gibbs-Markov Random Fields

Fig. 2. space by Patrick-Fisher's algorithm (solid line) and E (dotted line). Bayes error estimates for SONAR data transformed to IO-dimensional high-dimensional data these results might be more in favor of E.) This is a result of the fact that each iteration of simplex requires that the samples be transformed to the low-dimensional space, and then the Bayes error estimated in that space, which...