Related papers: Optimal concentration inequalities for dynamical s…
We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_\alpha$ for $\alpha \in [1, 2]$. We establish…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…
We show that any probability measure satisfying a Matrix Poincar\'e inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carr\'e du champ…
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…
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
Sharp constants for an inequality of Poincar\'e type is studied. The problem is solved by using optimal control theory.
We discuss the Lieb-Thirring inequality for periodic systems, which has the same optimal constant as the original inequality for finite systems. This allows us to formulate a new conjecture about the value of its best constant. To…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…
We obtain some important fundamental inequalities concerning the long time behavior of high order derivatives for solutions of some dissipative systems in terms of their $L^2$ algebraic decay. Some of these inequalities have not been…
For various classes of Lipschitz functions we provide dimension free concentration inequalities for infinitely divisible random vectors with independent components and finite exponential moments.
We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain…
This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A…
This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double…
We use a dynamical systems approach to study thawing quintessence models, using a multi-parameter extension of the exponential potential which can approximate the form of typical thawing potentials. We impose observational constraints using…