标题： 随机杨塔和主要扩张多模圆映射的淬火相关性衰减 显示英文标题

标题： Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps

摘要： 在本文中，我们研究由一族映射$\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in [-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\ (\mathrm{mod }\ 1),$ 生成的随机动力系统$f_\omega^n$，其中$\xi: \mathbb S^1 \to \mathbb R$是一个非退化的映射，$a\in [0,1)$，和$\alpha,\varepsilon>0$。 固定常数$c\in (0,1)$，我们证明当$\alpha$足够大且对于$\varepsilon > \alpha^{-1+c},$，随机动力系统$f_\omega^n$展现出随机 Young 阶梯结构和淬火相关性衰减。 显示英文摘要

摘要： In this paper, we study the random dynamical system $f_\omega^n$ generated by a family of maps $\{f_{\omega_0}: \mathbb{S}^1 \to \mathbb{S}^1\}_{\omega_0 \in [-\varepsilon,\varepsilon]},$ $f_{\omega_0}(x) = \alpha \xi (x+\omega_0) +a\ (\mathrm{mod }\ 1),$ where $\xi: \mathbb S^1 \to \mathbb R$ is a non-degenerated map, $a\in [0,1)$, and $\alpha,\varepsilon>0$. Fixing a constant $c\in (0,1)$, we show that for $\alpha$ sufficiently large and for $\varepsilon > \alpha^{-1+c},$ the random dynamical system $f_\omega^n$ presents a random Young tower structure and quenched decay of correlations.