Related papers: On Dropping Needles and WiFi Link Crossing
We are motivated by the problem of impromptu or as- you-go deployment of wireless sensor networks. As an application example, a person, starting from a sink node, walks along a forest trail, makes link quality measurements (with the…
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope $\gamma-\epsilon$, where $\gamma$…
We study a class of nearest-neighbor discrete time integer random walks introduced by Zerner, the so called multi-excited random walks. The jump probabilities for such random walker have a drift to the right whose intensity depends on a…
The Deffuant model is a spatial stochastic model for the dynamics of opinions in which individuals are located on a connected graph representing a social network and characterized by a number in the unit interval representing their opinion.…
Offloading of cellular traffic through a wireless local area network (WLAN) is theoretically evaluated. First, empirical data sets of the locations of WLAN internet access points are analyzed and an inhomogeneous Poisson process consisting…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…
We study a model of multi-excited random walk with non-nearest neighbour steps on $\mathbb Z$, in which the walk can jump from a vertex $x$ to either $x+1$ or $x-i$ with $i\in \{1,2,\dots,L\}$, $L\ge 1$. We first point out the multi-type…
Recently, the classical configuration model for random graphs with given degree distribution has been extensively used as a null model in contraposition to real networks with the same degree distribution. In this paper, we briefly review…
We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by…
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…
We investigate the problem of disseminating broadcast messages in wireless networks with time-varying links from a percolation-based perspective. Using a model of wireless networks based on random geometric graphs with dynamic on-off links,…
In this paper, we propose a methodology for estimating the crowd speed using WiFi devices without relying on people to carry any device. Our approach not only enables speed estimation in the region where WiFi links are, but also in the…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
We consider a state-dependent, time-dependent, discrete random walks $X_t^{\{a_n\}}$ defined on natural numbers $\mathbb{N}$ (bent to a "stair" in $\mathbb{N}^2$) where the random walk depends on input of a positive deterministic sequence…