Related papers: Random walks on complex trees
The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase…
Community assembly is studied using individual-based multispecies models. The models have stochastic population dynamics with mutation, migration, and extinction of species. Mutants appear as a result of mutation of the resident species,…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
Various real-life networks exhibit degree correlations and heterogeneous structure, with the latter being characterized by power-law degree distribution $P(k)\sim k^{-\gamma}$, where the degree exponent $\gamma$ describes the extent of…
It has been recently reported that the reciprocity of real-life weighted networks is very pronounced, however its impact on dynamical processes is poorly understood. In this paper, we study random walks in a scale-free directed weighted…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of $N$ nodes of degree $c \ge 3$. Starting from a random initial node at time $t=0$, at each time…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
A random walk on a regular tree (or any non-amenable graph) has positive speed. We ask whether such a walk can be slowed down by applying carefully chosen time-dependent permutations of the vertices. We prove that on trees the random walk…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…
It is natural to expect that nonbacktracking random walk will mix faster than simple random walks, but so far this has only been proved in regular graphs. To analyze typical irregular graphs, let $G$ be a random graph on $n$ vertices with…