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We present new criteria, based on commutator methods, for the strong mixing property of discrete flows $\{U^N\}_{N\in\mathbb Z}$ and continuous flows $\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ induced by unitary operators $U$ and self-adjoint…
In this paper we develop a quantitative Harris theorem with effective control over the constants. A benefit of our methodology is the decoupling of the small set and Lyapunov-Foster Drift conditions. Our methodology allows any small set and…
We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space…
In a previous paper we determined one dimensional distributions of a stationary field with linear regressions and quadratic conditional variances under a linear constraint on the coefficients of the quadratic expression. In this paper we…
We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…
We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.
A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and non irreducible Markov chains…
Higher-order scalar-tensor theories having an instantaneous mode do not develop the Ostrogradsky instability even if a seemingly dangerous mode is present. Such theories satisfy only partially the degeneracy conditions that are usually…
For a strictly stationary sequence of random vectors in $\mathbb{R}^d$ we study convergence of partial sum processes to L\'evy stable process in the Skorohod space with $J_1$-topology. We identify necessary and sufficient conditions for…
We introduce new first-order necessary conditions for mathematical programs with complementarity constraints (MPCCs), which lie between strong and M-stationarity and have a relatively simple description. We show that they hold for local…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
We show that the main features of the pattern of fermion masses and mixing can be expressed in terms of simple relations among weak-basis invariants. In the quark sector, we identify the weak-basis invariants which signal the observed…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…
We consider the Navier--Stokes--Fourier system in a bounded domain $\Omega \subset R^d$, $d=2,3$, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative…
In this paper I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature,…
We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…
For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…