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 |
References:
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