Limit Theorems for Dispersing Billiards with Cusps |
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Authors: | P Bálint N Chernov D Dolgopyat |
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Institution: | 1.Institute of Mathematics,Budapest University of Technology and Economics,Budapest,Hungary;2.Department of Mathematics,University of Alabama at Birmingham,Birmingham,USA;3.Department of Mathematics,University of Maryland,College Park,USA |
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Abstract: | Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-classical central limit theorem holds, with a scaling factor of \({\sqrt{n\log n}}\) replacing the standard \({\sqrt{n}}\) . We also derive the respective Weak Invariance Principle, and we identify the class of observables for which the classical CLT still holds. |
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