Related papers: An invariance principle for Az\'{e}ma martingales

This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…

We give an explicit arithmetical condition which guarantees the existence of the unstable manifold of the MacKay approximate renormalisation scheme for the breakup of invariant tori in one and a half degrees of freedom Hamiltonian systems,…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general c\`adl\`ag semimartingales taking values in Lie groups are defined and investigated. In order to enlarge the class of possible symmetries…

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive…

In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…

We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality…

We prove a martingale triangular array generalization of the Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain…

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…

We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…

We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…

This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.

In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA. The Reduction Principle is proved for EPCAG. The structure of the set of solutions is specified. We establish…

A new electronic structure principle, viz., the principle of electrophilicity equalization is proposed. An analytical justification as well as a numerical support for the same is provided.

We seek to establish qualitative convergence results to a general class of evolution PDEs described by gradient flows in optimal transportation distances. These qualitative convergence results come from dynamical systems under the general…

In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an…

Az\'{e}ma associated with an honest time L the supermartingale $Z_{t}^{L}=\mathbb{P}[L>t|\mathcal{F}_{t}]$ and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic…

We prove a logarithmic convexity result for exponentially weighted $L^2$-norms of solutions to electromagnetic Schr\"odinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique…

We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…