# Stochastic acceleration in a random time-dependent potential

2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : We study the long time behaviour of the speed of a particle moving in $\mathbb{R}^d$ under the influence of a random time-dependent potential representing the particle's environment. The particle undergoes successive scattering events that we model with a Markov chain for which each step represents a collision. Assuming the initial velocity is large enough, we show that, with high probability, the particle's kinetic energy $E(t)$ grows as $t^{\frac25}$ when $d>5$.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01061294
Contributor : Emilie Soret <>
Submitted on : Sunday, September 7, 2014 - 11:12:50 AM
Last modification on : Tuesday, July 3, 2018 - 11:41:20 AM
Long-term archiving on : Monday, December 8, 2014 - 10:06:34 AM

### Files

Markov-asymp2014_V2-01.pdf
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### Identifiers

• HAL Id : hal-01061294, version 1
• ARXIV : 1409.2098

### Citation

Emilie Soret, Stephan de Bièvre. Stochastic acceleration in a random time-dependent potential. Stochastic Processes and their Applications, Elsevier, 2015, 125, pp.2752-2785. ⟨hal-01061294⟩

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