A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...

Abstract. This article extends the Generalized Asypmtotic Equipartition Property of Networked Data Structures to cover the Wireless Sensor Network modelled as coloured geometric random graph (CGRG). The main techniques used to prove this result remains large deviation principles for properly defined empirical measures on coloured geometric random graphs. Application of the result to some case s...

Exploiting the coherent medium approximation, I investigate a random walk on objects distributed randomly in continuous space when jump rate depends distance between two adjacent objects. In one dimension, it is shown that decays exponentially long limit, non-diffusive to diffusive transition occurs as density of sites increased. three dimensions, exists has super Gaussian decay.

We consider graphs obtained by placing n points at random on a unit sphere in R, and connecting two points by an edge if they are close to each other (e.g., the angle at the origin that their corresponding unit vectors make is at most π/3). We refer to these graphs as geometric graphs. We also consider a complement family of graphs in which two points are connected by an edge if they are far aw...

We study the mixing time of random graphs in the d-dimensional toric unit cube [0, 1] generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights, drawn from s...

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ...

In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.