Displaying similar documents to “Random matrices and permutations, matrix integrals and integrable systems”

Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case

Michael M. Erlihson, Boris L. Granovsky (2008)

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

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We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ∼ , →∞, >0, where is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations...

Planar Lorentz process in a random scenery

Françoise Pène (2009)

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

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We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by...