Median, Concentration and Fluctuation for Lévy Processes

正弦Gordon测度在拓扑多孤子流形附近的集中与波动

Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold

研究正弦Gordon测度在多孤子流形附近的集中与波动，揭示典型状态中孤子的分布特性。

Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks

We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize the behavior of variance as fluctuations propagate down chains, study the effect of side chains and feedback loops, and investigate the asymptotic behavior as one rate constant gets large. We also describe how the ideas can be applied to the study of methionine metabolism.

Some superconcentration inequalities for extrema of stationary Gaussian Processes

This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian concentration. The arguments rely on the hypercontractive approach developed by Chatterjee for superconcentration variance bounds. Some statistical illustrations complete the exposition.

On concentration inequalities and their applications for Gibbs measures in lattice systems

We consider Gibbs measures on the configuration space $S^{\mathbb{Z}^d}$, where mostly $d\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we have a Gaussian concentration bound, whereas in the Ising model (and related models) at sufficiently low temperature, we control all moments and have a stretched-exponential concentration bound. We then give several applications of these inequalities whereby we obtain various new results. Amongst these applications, we get bounds on the speed of convergence of…

Concentration bounds for entropy estimation of one-dimensional Gibbs measures

We obtain bounds on fluctuations of two entropy estimators for a class of one-dimensional Gibbs measures on the full shift. They are the consequence of a general exponential inequality for Lipschitz functions of n variables. The first estimator is based on empirical frequencies of blocks scaling logarithmically with the sample length. The second one is based on the first appearance of blocks within typical samples.

Fluctuation bounds for chaos plus noise in dynamical systems

We are interested in time series of the form $y_{n} = x_{n} + ξ_{n}$ where ${x_{n}}$ is generated by a chaotic dynamical system and where $ξ_{n}$ models observational noise. Using concentration inequalities, we derive fluctuation bounds for the auto-covariance function, the empirical measure, the kernel density estimator and the correlation dimension evaluated along $y_{0}, ..., y_{n}$, for all $n$. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters.