Related papers: Groups, drift and harmonic measures
This work investigates the inverse drift problem in the one-dimensional parabolic equation with the final time data. The authors construct an operator first, whose fixed points are the unknown drift, and then apply it to prove the…
Consider a system of $n$ weakly interacting particles driven by independent Brownian motions. In many instances, it is well known that the empirical measure converges to the solution of a partial differential equation, usually called…
We consider a class of stochastic processes and establish its connection to $p$-harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a $p$-harmonic function, with an explicit convergence rate,…
In this paper, the familiar problems of free-fall motion and simple harmonic motion (SHM) are combined. The novel composite system passes from regular to chaotic behavior for increasing values of energy $E$. This system is a suitable…
The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. We are interested in an identification of those features, that are most relevant for the observed drift.…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
We present three measures of the dynamical coherence of channels, which are the generalization of several previous results. The measures are based on the generalized distance function between channels, which for example could be the…
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
A pedagogical and reasonably self-contained introduction to the measurement problems in quantum mechanics and their partial solution by environment-induced decoherence (plus some other important aspects of dcoherence) is given. The point…
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on…
Let $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, be a uniformly rectifiable set of dimension $n$. We show $E$ that has big pieces of boundaries of a class of domains which satisfy a 2-sided corkscrew condition, and whose connected components are…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the…
This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method…
We consider a stochastic functional differential equation with an arbitrary Lipschitz diffusion coefficient depending on the past. The drift part contains a term with superlinear growth and satisfying a dissipativity condition. We prove…
We propose a mechanism to describe how a physical quantity, which initially can take continuous values, is restricted within some discrete values after a measurement. As an example of the present theory, in which interplay between coherence…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…