Displaying similar documents to “Stationary measures and phase transition for a class of probabilistic cellular automata”

On uniqueness of G-measures and g-measures

Ai Fan (1996)

Studia Mathematica

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We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension...

Remarks on Palm Measures

Donald Geman, Joseph Horowitz (1973)

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

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Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit

Samuel Herrmann, Julian Tugaut (2012)

ESAIM: Probability and Statistics

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In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set...