Related papers: The P\'olya Web
We present a novel method for analysing socio-spatial segregation in cities by considering constraints imposed by transportation networks. Using a multilayered network approach, we model the interaction probabilities of socio-economic…
We introduce a set of techniques that allow for efficiently generating many independent random walks in the Massive Parallel Computation (MPC) model with space per machine strongly sublinear in the number of vertices. In this…
We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429--447]. We derive a strong law of large numbers for the random walks in a general…
We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the…
Our goal in this paper is to develop a practical framework for obtaining a uniform sample of users in an online social network (OSN) by crawling its social graph. Such a sample allows to estimate any user property and some topological…
Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using…
This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\mathbb{Z}^2$, started from the initial condition with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation functions of…
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…
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…
This paper shows the convergence of adele-valued random walks to an adelic L\'evy process under scaling limits. We use random walks on the $p$-adic numbers to construct random walks initially on the infinite product space, and use survival…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions…
We study random walks in i.i.d. random environments on $\mathbb{Z}^d$ when there are two basic types of vertices, which we call "blue" and "red". Each color represents a different probability distribution on transition probability vectors.…
The asymptotic behaviour of a generalised P\'olya--Eggenberger urn is well--known to depend on the spectrum of its replacement matrix: If its dominant eigenvalue $r$ is simple and no other eigenvalue is `large' in the sense that its real…
We consider a version of the classical P\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
We obtain the joint distribution $P_N (X, K|Z)$ of the location $X$ of a one-dimensional symmetric next neighbor random walk on the integer lattice, and the number of times the walk has visited a specified site $Z$. This distribution has a…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
We study topological properties of random closed curves on an orientable surface $S$ of negative Euler characteristic. Letting $\gamma_{n}$ denote the conjugacy class of the $n^{th}$ step of a simple random walk on the Cayley graph driven…