Related papers: A stable quantum Darmois-Skitovich theorem
A.M. Kagan introduced a class of distributions $\mathcal{D}_{m, k}$ in $\mathbb{R}^m$ and proved that if the joint distribution of $m$ linear forms of $n$ independent random variables belongs to the class $\mathcal{D}_{m, m-1}$, then the…
Let $X$ be an Abelian group of the form $X=\mathbb{R}^m\times K\times D$, where $m\geq 0$, $K$ is a compact totally disconnected group of the special form, $D$ is a discrete group. Let $\xi_i, i=1,2,...,n,n\geq 2,$ be independent random…
The stability of static solutions of the spherically symmetric, asymptotically flat Einstein-Vlasov system is studied using a Hamiltonian approach based on energy-Casimir functionals. The main result is a coercivity estimate for the…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…
We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…
Let $\Omega_p$ be the group of $p$-adic numbers, $ \xi_1$ and $\xi_2$ be independent random variables with values in $\Omega_p$ and distributions $\mu_1$ and $\mu_2$. Let $\alpha_j, \beta_j$ be topological automorphisms of $\Omega_p$.…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
In this work we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
Very recently we present a theory to discuss the nature of light and show that the quantization of light energy in vacuum can be derived directly from classical electromagnetic theory. In the theory a key concept of stability of statistical…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS) equation is investigated analytically and numerically. An effective stochastic equation belonging to the KPZ universality class is constructed by incorporating the…
We consider scattering of a free quantum particle on a singular potential with rather arbitrary shape of the support of the potential. In the classical limit $\hbar=0$ this problem reduces to the well known problem of chaotic scattering.…
We formulate and prove a {\it Local Stable Manifold Theorem\/} for stochastic differential equations (sde's) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and It\^o-type…
Recently, it has been shown that the quantum equilibrium distribution in the original Bohm's model is unstable and so it isn't a tenable physical theory [Proc. R. Soc. A 470 20140288 (2014)]. In this paper we show that a natural…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
A. Kagan introduced classes of distributions $\mathcal{D}_{m,k}$ in $m$-dimensional space $\mathbb{R}^m$. He proved that if the joint distribution of $m$ linear forms of $n$ independent random variables belong to the class…