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arXiv · 1902.08958

Necessary and sufficient condition for $\cM_2$-convergence to a L\'evy process for billiards with cusps at flat points

Paul Jung·Ian Melbourne·Françoise Pène·Paulo Varandas·Hong-Kun Zhang
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Abstract

We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding L\'evy process in the $\cM_1$ and $\cM_2$ Skorohod topologies has been studied in recent work. Here we show that certain sufficient conditions for $\cM_2$-convergence are also necessary.

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Paul Jung, Ian Melbourne, Françoise Pène, Paulo Varandas, Hong-Kun Zhang. 2019-02-24. Necessary and sufficient condition for $\cM_2$-convergence to a L\'evy process for billiards with cusps at flat points. https://arxiv.org/abs/1902.08958

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