When two scatterers intersect tangentially in a planar dispersing billiard domain, the particle can be trapped in the cuspoidal region. These phenomena are known to cause slow decay of correlations and non-standard limit theorems. In joint work with N. Chernov and D. Dolgopyat we have shown that the second moments of the appropriately normalized Birkhoff sums converge to a value which is twice the second moment of the limit distribution. In my talk I would like to describe this doubling effect and show that it arises in many other situations, in particular in an entirely probabilistic setting.
Convergence of moments in dispersing billiards with cusps
2016. 10. 06. 16:15