Annealed and Quenched Limit Theorems for Random Expanding Dynamical Systems

Abstract : In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more prob-abilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure invariance principle. We also discuss the quenched central limit theorem, dynamical Borel-Cantelli lemmas, Erdös-Rényi laws and concentration inequalities.
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Romain Aimino, Matthew Nicol, Sandro Vaienti. Annealed and Quenched Limit Theorems for Random Expanding Dynamical Systems. Probability Theory and Related Fields, Springer Verlag, 2015, 162 (1), pp.233-274. ⟨10.1007/s00440-014-0571-y⟩. ⟨hal-01126718⟩

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