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Perturbing transient random walk in a random environment with cookies of maximal strength

Elisabeth Bauernschubert (2013)

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

We consider a left-transient random walk in a random environment on ℤ that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.

Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique

Sandrine Roussel (2000)

Colloquium Mathematicae

The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let Q * k denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value k n for which the total variation norm between Q * k and π stays very close to 1 for k ≪ k n , and falls rapidly to a value close to 0 for k ≥ k n with a fall-off phase much shorter than k n . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...

Plurisubharmonic martingales and barriers in complex quasi-Banach spaces

Nassif Ghoussoub, Bernard Maurey (1989)

Annales de l'institut Fourier

We describe the geometrical structure on a complex quasi-Banach space X that is necessay and sufficient for the existence of boundary limits for bounded, X -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...

Poincaré inequalities and hitting times

Patrick Cattiaux, Arnaud Guillin, Pierre André Zitt (2013)

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

Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....

Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation

Hélène Guérin (2004)

ESAIM: Probability and Statistics

Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...

Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation

Hélène Guérin (2010)

ESAIM: Probability and Statistics


Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...

Pointwise ergodic theorems with rate and application to the CLT for Markov chains

Christophe Cuny, Michael Lin (2009)

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

Let T be Dunford–Schwartz operator on a probability space (Ω, μ). For f∈Lp(μ), p>1, we obtain growth conditions on ‖∑k=1nTkf‖p which imply that (1/n1/p)∑k=1nTkf→0 μ-a.e. In the particular case that p=2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic–Lin and Wu–Woodroofe....

Poisson boundary of triangular matrices in a number field

Bruno Schapira (2009)

Annales de l’institut Fourier

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.

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