For polynomially mixing billiards with cusps, Birkhoff sums of observables φ(x) = d(x,x0)^{-2/α} with tail index α satisfy stable laws whose index is a function of both α and the mixing exponent γ when γ ∈ (1/2,1) and α ∈ (0,2) excluding 1.
Weak convergence to
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Stable laws for heavy-tailed observables on polynomially mixing billiards
For polynomially mixing billiards with cusps, Birkhoff sums of observables φ(x) = d(x,x0)^{-2/α} with tail index α satisfy stable laws whose index is a function of both α and the mixing exponent γ when γ ∈ (1/2,1) and α ∈ (0,2) excluding 1.