Related papers: Excursion Set Theory for Correlated Random Walks
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
We present analytical results for the distribution of first hitting times of random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a finite size $N$. Starting from a random initial node at time $t=1$, at each time step…
We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^\chi$, while the transversal fluctuations, known as…
We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
Analyzing the mixing time of random walks is a well-studied problem with applications in random sampling and more recently in graph partitioning. In this work, we present new analysis of random walks and evolving sets using more…
We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as expectation of a functional of the…
In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…
We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately achieves first-passage, leaving the medium or it is absorbed. The Kubelka-Munk model describes a…
In this article we study the distribution of the number of points of a simple random walk, visited a given number of times (the k-multiple point range). In a previous article we had developed a graph theoretical approach which is now…