Related papers: The Distribution of Random Evolution in Erlang Sem…
In this paper we consider a large class of super-Brownian motions in $\mathbb{R}$ with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mass located outside a time-dependent interval $(-\delta…
We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
The purpose of this work is to find the time dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the scatterers are randomly placed. The…
Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…
We consider the mutual distribution of two linearly independent solutions y_1(x) and y_2(x) of the 1D Schroedinger equation with a random potential. Since individual distributions of $y_1$ and $y_2$ are log-normal, it is naturally to…
In this paper we consider a random walk of a particle in $\mathbb{R}^d$. Convergence of different transformations of trajectories of random flights with Poisson switching moments has been obtained by Davydov and Konakov, as well as…
We investigate the relation between the distributions appearing in the study of ergodic averages of parabolic flows (e.g. in the work of Flaminio-Forni) and the ones appearing in the study of the statistical properties of hyperbolic…
This paper develops an averaging technique based on the combination of the eigenfunction expansion method and the collaboration method to investigate the multiple scattering effect of the SH wave propagation in a porous medium. The…
We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables like current and activity pertain to the first class, which is composed by random variables that change whenever a jump in…
We provide a self-contained analysis, based entirely on pde methods, of the exponentially long time behavior of solutions to linear uniformly parabolic equations which are small perturbations of a transport equation with vector field having…
Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less or equal $2$, while delocalization is expected for hopping $V(r)$ decreasing with the distance slower or as $r^{-d}$, the localization…
We study the behavior of a semi-infinite monolayer, which is placed initially on a half of an infinite in both directions, ideal crystalline surface, and then evolves in time due to random motion of the monolayer particles. Particles…
We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…
We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…