Sábháilte in:
| Príomhchruthaitheoirí: | , , |
|---|---|
| Formáid: | Preprint |
| Foilsithe / Cruthaithe: |
2024
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| Ábhair: | |
| Rochtain ar líne: | https://arxiv.org/abs/2407.16632 |
| Clibeanna: |
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Clár na nÁbhar:
- We use a Poisson point process approach to prove distributional convergence to a stable law for non square-integrable observables $ϕ: [0,1]\to R$, mostly of the form $ϕ(x) = d(x,x_0)^{-\frac{1}α}$,$0<α\le 2$, on Gibbs-Markov maps. A key result is to verify a standard mixing condition, which ensures that large values of the observable dominate the time-series, in the range $1<α\le 2$. Stable limit laws for observables on dynamical systems have been established in two settings: ``good observables'' (typically Hölder) on slowly mixing non-uniformly hyperbolic systems and ``bad'' observables (unbounded with fat tails) on fast mixing dynamical systems. As an application we investigate the interplay between these two effects in a class of intermittent-type maps.