Related papers: On Dropping Needles and WiFi Link Crossing

We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth is random and its length equals lambda^{N-1}, with lambda<1. As lambda increases past a critical value lambda_c, the endpoint…

We investigate a relationship network of humans located in a metric space where relationships are drawn according to a distance-dependent probability density. The obtained spatial graph allows us to calculate the average separation of…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…

In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…

We study the effect of motion on disease spreading in a system of random walkers which additionally perform long-distance jumps. A small percentage of jumps in the agent motion is sufficient to destroy the local correlations and to produce…

We consider simple random walk on Z^d, d bigger or equal to 3. Motivated by the work of A.-S. Sznitman and the author in arXiv:1304.7477 and arXiv:1310.2177, we investigate the asymptotic behaviour of the probability that a large body gets…

We investigate crossing path probabilities for two agents that move randomly in a bounded region of the plane or on a sphere (denoted $R$). At each discrete time-step the agents move, independently, fixed distances $d_1$ and $d_2$ at angles…

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…

Consider a random medium consisting of points randomly distributed so that there is no correlation among the distances. This is the random link model, which is the high dimensionality limit (mean field approximation) for the euclidean…

This letter proposes a novel random medium access control (MAC) based on a transmission opportunity prediction, which can be measured in a form of a conditional success probability given transmitter-side interference. A transmission…

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…

The aim of this short article is to convey the basic idea of the original paper [3], without going into too much detail, about how to derive sharp asymptotics of the gyration radius for random walk, self-avoiding walk and oriented…

We study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently and identically distributed in a large domain, with a…

Keeler, Ross and Xia (2016) recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation…

Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…

We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…

Location information is often used as a proxy to infer the performance of a wireless communication link. Using a very simple model, this letter unveils a basic statistical relation between the location estimation uncertainty and wireless…

Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…