Related papers: Deviation and concentration inequalities for dynam…
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…
We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law conservation law. When the…
Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this…
The situation of the metastable phase decay on the several types of heterogeneous centers is considered. This publication directly continues " [email protected] get 0001104 ", " [email protected] get 0001108" and "…
We derive novel concentration inequalities that bound the statistical error for a large class of stochastic optimization problems, focusing on the case of unbounded objective functions. Our derivations utilize the following key tools: 1) A…
In this work, we consider the so-called correlated random walk system (also known as correlated motion or persistent motion system), used in biological modelling, among other fields, such as chromatography. This is a linear system which can…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…
We study the dynamics of density fluctuations in purely diffusive systems away from equilibrium. Under some conditions the static density correlation function becomes long-ranged. We then analyze this behavior in the framework of…
Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies,…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
This work presents numerical evidences that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance…
We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…