随机Ruelle扩张映射的淬火与退火平衡态及其应用

Quenched CLT for random toral automorphism

We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps.

复合泊松分布用于随机动力系统：基于概率近似的方法

Compound Poisson distributions for random dynamical systems using probabilistic approximations

本文通过概率分块近似，对一类随机动力系统证明了淬灭击中分布为复合泊松，采用退火Kac归一化，并应用于随机分段扩张系统，揭示周期与非周期点二分法的新视角。

随机洛伦兹气体的半淬火不变性原理——超越玻尔兹曼-格拉德极限

Semi-Quenched Invariance Principle for the Random Lorentz Gas -- Beyond the Boltzmann-Grad Limit

通过同步耦合多条洛伦兹轨迹，将随机洛伦兹气体的退火不变性原理沿快速提取子序列提升至淬火情形，适用于R^3中随机散射体环境。

Large deviations and central limit theorems for sequential and random systems of intermittent maps

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol, Török and Vaienti for random dynamical systems comprised of intermittent maps. Using recent work of Abdelkader and Aimino, Hella and Stenlund we extend the results of Nicol, Török and Vaienti on quenched central limit theorems (CLT) for centered observables over random compositions of intermittent maps: first by enlarging the parameter range over which the que…

Erratic behavior for 1-dimensional random walks in a Liouville quasi-periodic environment

We show that one-dimensional random walks in a quasi-periodic environment with Liouville frequency generically have an erratic statistical behavior. In the recurrent case we show that neither quenched nor annealed limit theorems hold and both drift and variance exhibit wild oscillations, being logarithmic at some times and almost linear at other times. In the transient case we show that the annealed Central Limit Theorem fails generically. These results are in stark contrast with the Diophantine case where the Central Limit Theorem with linear drift and variance was established by Sinai.

随机动力系统中有效的淬火线性响应

Effective quenched linear response for random dynamical systems

本文研究了非均匀扩展随机动力系统中有效的线性响应，探讨了其在CLT方差可微性和退化线性响应中的应用，提供了多种一维和高维映射示例。