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Knudsen gas in flat tire. (English) Zbl 1409.60048

Summary: 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.

MSC:

60F17 Functional limit theorems; invariance principles
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
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
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References:

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