Related papers: Occupation times on a comb with ramified teeth
The patterns of motion of mobile agents has received recently wide attention in the literature. There is a number of recent studies centered around the motion behavior of many agents ranging from albatrosses to human beings. Special…
We study continuous time quantum random walk on a comb with infinite teeth and show that the return probability to the starting point decays with time $t$ as $t^{-1}$. We analyse the diffusion along the spine and into the teeth and show…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
We analyze the covertime of a biased random walk on the random graph $G_{n,p}$. The walk is biased towards visiting vertices of low degree and this makes the covertime less than in the unbiased case
We study the occupation measure of various sets for a symmetric transient random walk in $Z^d$ with finite variances. Let $\mu^X_n(A)$ denote the occupation time of the set $A$ up to time $n$. It is shown that $\sup_{x\in…
Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they…
We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of "valleys" of height…
Assume that $T$ is a conservative ergodic measure preserving transformation of the infinite measure space $(X,\mathcal{A},\mu)$.We study the asymptotic behaviour of occupation times of certain subsets of infinite measure. Specifically, we…
We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
The density conjecture for activated random walk on the interval was recently resolved using a new tool called layer percolation. As a step towards understanding how layer percolation extends to activated random walk on more complex graphs,…
The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous…
We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large…
Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these…
This chapter is a contribution in the "Handbook of Applications of Chaos Theory" ed. by Prof. Christos H Skiadas. The chapter is organized as follows. First we study the statistical properties of combs and explain how to reduce the effect…
We consider particle systems in locally compact Abelian groups with particles moving according to a process with symmetric stationary independent increments and undergoing one and two levels of critical branching. We obtain long time…
We study a transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure…