Related papers: Exact calculations of first-passage quantities on …
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…
The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…
This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approximate specific queues on R with one-sided L\'evy input, such as…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
We study the problem of random search in finite networks with a tree topology, where it is expected that the distribution of the first-passage time F(t) decays exponentially. We show that the slope of the exponential tail is independent of…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods,…
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact…
In general, the power-law degree distribution has profound influence on various dynamical processes defined on scale-free networks. In this paper, we will show that power-law degree distribution alone does not suffice to characterize the…
First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under restart mechanism. Emanating from the canonical diffusion problem by Evans and Majumdar, restart has been shown to…
These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…
In this note, we present some ideas for describing the distributions of the running maximum/minimum, first passage times and telegraphic meanders. Explicit formulae for joint distribution of the extrema, the number of velocity switches and…
Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent $\gamma$ of power-law degree…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…