Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 308, Issue 2, Pages 479-510Publisher
SPRINGER
DOI: 10.1007/s00220-011-1342-6
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Funding
- Hungarian Academy of Sciences
- Hungarian National Fund for Scientific Research (OTKA) [F60206, K71693]
- NSF [DMS-0969187, DMS-0555743]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0969187] Funding Source: National Science Foundation
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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 root n log n replacing the standard root 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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