Variational principle for Gibbs point processes with finite range interaction

Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and asymptotic normality. We also consider its finite-sample properties in a simulation study.

Variational Principle for Fuzzy Gibbs Measures

In this paper we study a large class of renormalization transformations of measures on lattices. An image of a Gibbs measure under such transformation is called a fuzzy Gibbs measure. Transformations of this type and fuzzy Gibbs measures appear naturally in many fields. Examples include the hidden Markov processes (HMP), memoryless channels in information theory, continuous block factors of sym...

Parametric estimation of pairwise Gibbs point processes with infinite range interaction

The Variational Principle for Gibbs States Fails on TreesRobert

We show how the variational principle for Gibbs States (which says that for the d{ dimensional cubic lattice, the set of translation invariant Gibbs States is the same as the set of translation invariant measures which maximize entropy minus energy and moreover that this quantity corresponds to the pressure) fails for nearest neighbor nite state statistical mechanical systems on the homogeneous...

On the Variational Principle for Generalized Gibbs Measures

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamic formalism for generalized Gibbs states will be discussed. A new class of intuitively Gibbs measures is introduced, and a typical example is studied. Finally, we present a new example of a non-Gibbsian measure arising from an industrial ap...