The Annals of Applied Probability

Knudsen gas in flat tire

Krzysztof Burdzy and Carl-Erik Gauthier

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We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero, properly rescaled angular component of the light ray position converges in distribution to a diffusion whose parameters (diffusivity and drift) are given explicitly in terms of the tube width.

Article information

Ann. Appl. Probab., Volume 29, Number 1 (2019), 217-263.

Received: January 2018
Revised: June 2018
First available in Project Euclid: 5 December 2018

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 37D50: Hyperbolic systems with singularities (billiards, etc.) 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G42: Martingales with discrete parameter 60G44: Martingales with continuous parameter 60J05: Discrete-time Markov processes on general state spaces 60J25: Continuous-time Markov processes on general state spaces

Stochastic billiard invariance principle Knudsen random walk cosine distribution


Burdzy, Krzysztof; Gauthier, Carl-Erik. Knudsen gas in flat tire. Ann. Appl. Probab. 29 (2019), no. 1, 217--263. doi:10.1214/18-AAP1412.

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