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Markovian perturbation, response and fluctuation dissipation theorem

Amir Dembo, Jean-Dominique Deuschel (2010)

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

We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...

Martin boundary associated with a system of PDE

Allami Benyaiche, Salma Ghiate (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. ▵ 2 ϕ = 0 ) and for non negative solutions of the equation ▵ 2 ϕ = ϕ .

Mathematical model of mixing in Rumen

Wiesław Szlenk (1996)

Applicationes Mathematicae

A mathematical model of mixing food in rumen is presented. The model is based on the idea of the Baker Transformation, but exhibits some different phenomena: the transformation does not mix points at all in some parts of the phase space (and under some conditions mixes them strongly in other parts), as observed in ruminant animals.

Maximal brownian motions

Jean Brossard, Michel Émery, Christophe Leuridan (2009)

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

Let Z=(X, Y) be a planar brownian motion, 𝒵 the filtration it generates, andBa linear brownian motion in the filtration 𝒵 . One says thatB(or its filtration) is maximal if no other linear 𝒵 -brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration 𝒵 asZ....

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