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arXiv · 1610.06123

Decay of correlations and laws of rare events for transitive random maps

Vitor Araujo·Hale Aytac
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Abstract

We show that a uniformly continuous random perturbation of a transitive map defines an aperiodic Harris chain which also satisfies Doeblin's condition. As a result, we get exponential decay of correlations for suitable random perturbations of such systems. We also prove that, for transitive maps, the limiting distribution for Extreme Value Laws (EVLs) and Hitting/Return Time Statistics (HTS/RTS) is standard exponential. Moreover, we show that the Rare Event Point Process (REPP) converges in distribution to a standard Poisson process.

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Vitor Araujo, Hale Aytac. 2017-04-19. Decay of correlations and laws of rare events for transitive random maps. https://doi.org/10.1088/1361-6544%2Faa64e8

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