Related papers: Harmonic problems arising from continuous time ran…
In this paper we study random walks on dynamical random environments in $1 + 1$ dimensions. Assuming that the environment is invariant under space-time shifts and fulfills a mild mixing hypothesis, we establish a law of large numbers and a…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set…
Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
We investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. At each jump, the random walker is subject to a drift that depends on whether it is…
We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic, but strongly chaotic, evolution. We prove that for almost all initial conditions of the environment the walk satisfies the CLT.
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the…
In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Consider the dynamic environment governed by a Poissonian field of independent particles evolving as simple random walks on $\mathbb{Z}^d$. The random walk on random walks model refers to a particular stochastic process on $\mathbb{Z}^d$…
We investigate the impact of coherent control errors on quantum state evolution by deriving a general norm inequality based on Gronwall's lemma. This inequality provides an explicit upper bound on the deviation between an ideal quantum…
We propose a novel heuristic quantum algorithm for the Minimum Vertex Cover (MVC) problem based on continuous-time quantum walks (CTQWs). In this framework, the coherent propagation of a quantum walker over a graph encodes its structural…