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An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying…

Quantum Physics · Physics 2019-11-13 Gastón García-Calderón , Roberto Romo , Miguel Ángel Terán

This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…

Networking and Internet Architecture · Computer Science 2012-10-05 Guoqiang Mao , Brian Do Anderson

In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…

Data Analysis, Statistics and Probability · Physics 2024-07-16 Taki Kirouani

The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

Probability · Mathematics 2019-02-05 Klemens Taglieber , Uta Freiberg

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…

Machine Learning · Computer Science 2012-03-19 Ping Li , Michael W. Mahoney , Yiyuan She

Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…

Probability · Mathematics 2025-11-10 Han Huang , Pakawut Jiradilok , Elchanan Mossel

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

Machine Learning · Computer Science 2026-04-10 Han Huang , Pakawut Jiradilok , Elchanan Mossel

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…

Classical Analysis and ODEs · Mathematics 2015-08-20 Jonathan M. Borwein , Armin Straub , Christophe Vignat

Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…

Statistical Mechanics · Physics 2013-03-21 Alberto Antonioni , Marco Tomassini

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…

Computational Geometry · Computer Science 2011-08-23 Esther M. Arkin , Antonio Fernandez Anta , Joseph S. B. Mitchell , Miguel A. Mosteiro

A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…

Physics and Society · Physics 2015-05-20 Ernesto Estrada , Matthew Sheerin

A variety of transport processes in natural and man-made systems are intrinsically random. To model their stochasticity, lattice random walks have been employed for a long time, mainly by considering Cartesian lattices. However, in many…

Statistical Mechanics · Physics 2023-06-14 Daniel Marris , Seeralan Sarvaharman , Luca Giuggioli

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

Statistical Mechanics · Physics 2017-04-03 A. V. Nazarenko , V. Blavatska

Seamless redundancy can be profitably exploited to improve predictability of wireless networks in general and, in particular, IEEE 802.11. According to this approach, packets are transmitted by senders on two (or more) channels at the same…

Networking and Internet Architecture · Computer Science 2022-11-01 Gianluca Cena , Stefano Scanzio , Adriano Valenzano

Motivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations.…

Probability · Mathematics 2015-02-19 Christian Hirsch

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

Statistical Mechanics · Physics 2007-05-23 Naoki Masuda , Norio Konno

We introduce a conditional pair distribution function (CPDF) which characterizes the probability density of finding an object (e.g., a particle in a fluid) to certain distance of other, with each of these two having a nearest neighbor to a…

Statistical Mechanics · Physics 2015-03-19 René D. Rohrmann , Ernesto Zurbriggen

Directional beamforming will play a paramount role in 5G and beyond networks in order to combat the higher path losses incurred at millimeter wave bands. Appropriate modeling and analysis of the angles and distances between transmitters and…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Social and Information Networks · Computer Science 2016-05-04 Weiyu Huang , Alejandro Ribeiro