Related papers: Random walk on Sierpinski-type multifractals
Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…
We consider a model of loop-erased random walks on the finite pre-Sierpinski gasket which permits rigorous analysis. We prove the existence of the scaling limit and show that the path of the limiting process is almost surely self-avoiding,…
Spherically symmetric random walks in arbitrary dimension $D$ can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of…
We analyze a random walk strategy on undirected regular networks involving power matrix functions of the type $L^{\frac{\alpha}{2}}$ where $L$ indicates a `simple' Laplacian matrix. We refer such walks to as `Fractional Random Walks' with…
We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on $\mathbb{Z}^d$, in dimension $d\ge 5$, both in the upward and downward directions. The results are analogous to those we obtained for…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
We show connection between Dyck paths with peaks of bounded height and random walks. The correspondence between a certain class of random walks and such Dyck paths allows us to develop a probabilistic perspective on Chebyshev polynomials.
As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of…
We relate some basic constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
In this work, the probability of return for random walks on $\mathbb{Z}$, whose increment is given by the $k$-bonacci sequence, is determined. Also, the Hausorff, packing and box-counting dimensions of the set of these walks that return an…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…
We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with…
We study analytically the order statistics of a time series generated by the successive positions of a symmetric random walk of n steps with step lengths of finite variance \sigma^2. We show that the statistics of the gap d_{k,n}=M_{k,n}…
We study once-reinforced random walk (ORRW) on $\mathbb Z$. For this model, we derive limit results on all moments of its range using Tauberian theory.
We consider the average number B_m(t) of bonds traversed exactly m times by a t step simple random walk. We determine B_m(t) explicitly in the scaling limit t -> oo with m/sqrt(t) fixed in dimension d=1 and m/log(t) fixed in dimension d=2.…