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Infinite queueing systems with tree structure

Lucie Fajfrová (2006)

Kybernetika

We focus on invariant measures of an interacting particle system in the case when the set of sites, on which the particles move, has a structure different from the usually considered set ℤ d . We have chosen the tree structure with the dynamics that leads to one of the classical particle systems, called the zero range process. The zero range process with the constant speed function corresponds to an infinite system of queues and the arrangement of servers in the tree structure is natural in a number...

Infinite system of Brownian balls with interaction: the non-reversible case

Myriam Fradon, Sylvie Rœlly (2007)

ESAIM: Probability and Statistics

We consider an infinite system of hard balls in d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.

Interacting brownian particles and Gibbs fields on pathspaces

David Dereudre (2003)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Interacting Brownian particles and Gibbs fields on pathspaces

David Dereudre (2010)

ESAIM: Probability and Statistics

In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.

Intermittency and ageing for the symbiotic branching model

Frank Aurzada, Leif Döring (2011)

Annales de l'I.H.P. Probabilités et statistiques

For the symbiotic branching model introduced in [Stochastic Process. Appl.114 (2004) 127–160], it is shown that ageing and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with brownian potential. Some refinements to more general (also infinite range) kernels of recent ageing results of [Ann. Inst. H. Poincaré...

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