Related papers: Random Walks Across Dimensions: Exploring Simplici…
The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements.…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously…
One can define a random walk on a hypercubic lattice in a space of integer dimension $D$. For such a process formulas can be derived that express the probability of certain events, such as the chance of returning to the origin after a given…
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our…
Reflected random walk in higher dimension arises from an ordinary random walk (sum of i.i.d. random variables): whenever one of the reflecting coordinates becomes negative, its sign is changed, and the process continues from that modified…
We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…
We survey recent results on some one- and two-dimensional patterns generated by random permutations of natural numbers. In the first part, we discuss properties of random walks, evolving on a one-dimensional regular lattice in discrete time…
The following is an introduction to the study of higher walks, by which we mean a family of higher-dimensional extensions of Todorcevic's method of walks on the ordinals. After a brief review of this method, including, for example,…
In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a…
In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call…
Studying how we explore the world in search of novelties is key to understand the mechanisms that can lead to new discoveries. Previous studies analyzed novelties in various exploration processes, defining them as the first appearance of an…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…
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 measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility,…
To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension.…