Annealed and quenched limit theorems for random expanding dynamical systems

By Romain Aimino, Matthew Nicol, Sandro Vaienti. 2013

86 citations recorded by the source corpus.

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic 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.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/455a74f19064926f41cb8a306ac81b48d9aa7ba8

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In Mathematical Physics

1. Matthew Nicol
2. N. Haydn
3. Andrei Török
4. Sandro Vaienti
5. Ian Melbourne
6. Alexander I. Bufetov
7. E. Rio

Citations in the corpus

• A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems (2017, unknown): “The corresponding limit laws with respect to μ̂ are typically called annealed limit laws; see [2] and references therein for recent results in this framework.”
• Almost sure invariance principle for sequential and non-stationary dynamical systems (2014, background): “If the density of μ with respect to Lebesgue measure m is strictly bounded below, dμ dm ≥ c > 0 for some constant c , then (cid:12) P n φ (cid:12) BV ≤ Cθ n φ (cid:12) BV implies exponential decay in the BV norm versus L 1 ( μ ); see for instance [9, Proposition 3.1].”