Related papers: Statistical stability and linear response for rand…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of $C^2$…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
Contact-drop dispensing is central to many small-scale applications, such as direct-scanning probe lithography and micromachined fountain-pen techniques. Accurate and controllable dispensing required for nanometer-resolved surface…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
In this paper, we obtain some preliminary results on stochastic control theory for time-varying linear systems both continuous and discrete, and further apply to aperiod sample-data linear systems. The Ito's lemma is utilized in this…
The unpredictability of chaotic nonlinear dynamics leads naturally to statistical descriptions, including probabilistic limit laws such as the central limit theorem and large deviation principle. A key tool in the Nagaev-Guivarc'h spectral…
We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over $\mathbb{C}$ attached to character polynomials. Our approach interprets the stabilization as a probabilistic…
Structured on the paradigmatic Navier-Stokes flow model, we study a stochastically forced Taylor-Couette system in the narrow gap limit, in order to analyze the simultaneous impact of a non-conserved (Gaussian) force and a nonlinear…
We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…
In the present paper we analyze the linear stability of a hierarchical size-structured population model where the vital rates (mortality, fertility and growth rate) depend both on size and a general functional of the population density…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We show that a $\mathrm{GL}(d,\mathbb{R})$ cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov…
In this paper, we introduce a joint central limit theorem (CLT) for specific bilinear forms, encompassing the resolvent of the sample covariance matrix under an elliptical distribution. Through an exhaustive exploration of our theoretical…