Optimal concentration inequalities for dynamical systems

Moment bounds and concentration inequalities for slowly mixing dynamical systems

We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalous diffusion in the form of a stable law or a central limit theorem with nonstandard scaling $(n\log n)^{1/2}$.

Fluctuations of observables in dynamical systems: from limit theorems to concentration inequalities

We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable laws, and large deviations. Next, we describe a new branch in the study of probabilistic properties of dynamical systems, namely concentration inequalities. They allow to describe the fluctuations of very general observables and to get bounds rather than limit laws. We end up with two sections: one gathering various open problems, notably on random dynamica…

Deviation and concentration inequalities for dynamical systems with subexponential decay of correlation

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.

随机动力系统中的集中不等式

Concentration inequalities for random dynamical systems

本文在弱平均收缩条件下，建立随机动力系统中观测量的集中不等式，研究时间平均同步、经验测度等随机量的偏差界，并给出有限时间Lyapunov指数的集中不等式。

Concentration inequalities for sequential dynamical systems of the unit interval

We prove a concentration inequality for sequential dynamical systems of the unit interval enjoying an exponential loss of memory in the BV norm, and we investigate several of its consequences. In particular, this covers compositions of $β$-transformations, with all $β$ lying in a neighborhood of a fixed $β_{\star} > 1$ and systems satisfying a covering type assumption.

超临界Dyson模型的集中不等式与转移算子

Concentration inequalities and Transfer operators for supercritical Dyson models

该研究将铁磁Dyson模型的既有结果拓展到近临界与强相互作用区域，并在整个超临界区域内为唯一的无穷体积Gibbs测度建立了高斯集中界，推进了超临界Dyson模型的相关理论研究。