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Excited against the tide: a random walk with competing drifts

Mark Holmes (2012)

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

We study excited random walks in i.i.d. random cookie environments in high dimensions, where the k th cookie at a site determines the transition probabilities (to the left and right) for the k th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that the limiting...

Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials.

Céline Baranger, Clément Mouhot (2005)

Revista Matemática Iberoamericana

This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator...

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