Gibbs Point Processes Research Articles

A Gibbs point process on a finite series of circles:the insertion of the primary roots of maize around the stem

An extension of the Gibbs model is proposed in order to analyse circular data distributed on a finite number of concentric circles. This model is used to study the angular distribution of the primary roots of maize around the stem, each internode being modelled as a circle. The roots on a single internode or on two successive internodes interact, the interaction between roots on a single internode being higher than that between roots on two successive internodes.

Limit theorem and large deviation principle for the Voronoi tessellation generated by a Gibbs point process

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.

Limit theorem and large deviation principle for the Voronoi tessellation generated by a Gibbs point process

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.

Second‐order Characteristics for Stochastic Structures Connected with Gibbs Point Processes

AbstractThe points of stationary and isotropic GIBBS point process are marked by exp(corresponding local energy). For the mean mark and two mark product density functions very simple formulae are true which contain the intensity and the pair potential function of the process. Furthermore, there is a close connection between the pair correlation function of the process and the covariance function of the random field given by the conditional intensity.

Random graph approach to Gibbs processes with pair interaction

This study was motivated by the observation that, in a broad class of cases, the distribution of classical Gibbs point processes in Rd governed by ‘pair potential’, can be obtained as the equilibrium distribution of a Markov chain of point processes in Rd. Our analysis of this Markov chain is based on its imbedding in an infinite random graph. A condition of ergodicity of the chain is given in terms of the ‘absence of percolation’ in the graph, and this can be checked in simpler cases. The embedding also suggests a stochastic construction for the equilibrium distribution in question.

Statistical Inference for a Gibbs Point Process of Mutually Non‐Intersecting Discs

AbstractFor a Gibbs point process of mutually non‐intersecting discs a parameter estimation method is suggested. It is applied to a pattern of positions of beadlet anemones, for which, until now, no appropriate Gibbs process model has been found.

The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity

The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity