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Necessary and sufficient condition for cM₂-convergence to a L\'evy process for billiards with cusps at flat points
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Necessary and sufficient condition for cM₂-convergence to a L\'evy process for billiards with cusps at flat points
classification
math.DS
keywords
convergencebilliardsnecessaryprocesssufficientbeencertainclass
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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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