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We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…

Probability · Mathematics 2024-04-23 Peter Gracar , Lukas Lüchtrath , Peter Mörters

We give numerically tractable, explicit integral expressions for the distribution of the signal-to-interference-and-noise-ratio (SINR) experienced by a typical user in the down-link channel from the k-th strongest base stations of a…

Networking and Internet Architecture · Computer Science 2014-01-17 Holger Paul Keeler , Bartlomiej Blaszczyszyn , Mohamed Kadhem Karray

A hyperscaling relation for the critical exponents of absorbing phase transitions is tested in the bosonic pair contact process with diffusion. To this end spreading is considered, i.e. the time evolution out of an initial seed. It is shown…

Statistical Mechanics · Physics 2016-08-31 Matthias Paessens

Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…

Disordered Systems and Neural Networks · Physics 2015-06-15 Kun Zhao , Ginestra Bianconi

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…

Statistical Mechanics · Physics 2014-10-28 N. A. M. Araújo , P. Grassberger , B. Kahng , K. J. Schrenk , R. M. Ziff

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…

Statistical Mechanics · Physics 2015-05-27 F. L. Santos , Ronald Dickman , U. L. Fulco

In this paper, we study a model of long-range site percolation on graphs of bounded degree, namely the Boolean percolation model. In this model, each vertex of an infinite connected graph is the center of a ball of random radius, and…

Probability · Mathematics 2025-11-25 Corentin Faipeur

In recent years, neural networks have increasingly been employed to identify critical points of phase transitions. For the tricritical directed percolation model, its steady-state configurations encompass both first-order and second-order…

Statistical Mechanics · Physics 2024-11-08 Feng Gao , Jianmin Shen , Shanshan Wang , Wei Li , Dian Xu

We consider a random connection model (RCM) $\xi$ driven by a Poisson process $\eta$. We derive exponential moment bounds for an arbitrary cluster, provided that the intensity $t$ of $\eta$ is below a certain critical intensity $t_T$. The…

Probability · Mathematics 2026-02-05 Mikhail Chebunin , Günter Last

Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact…

Physics and Society · Physics 2021-02-03 Angélica S. Mata

This paper proposes a novel approach for computing the meta distribution of the signal-to-interference-plus-noise ratio (SINR) for the downlink transmission in a wireless network with Rayleigh fading. The novel approach relies on an…

Information Theory · Computer Science 2023-02-08 Yujie Qin , Mustafa A. Kishk , Mohamed-Slim Alouini

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links…

Statistical Mechanics · Physics 2018-05-29 Jens Karschau , Marco Zimmerling , Benjamin M. Friedrich

We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…

Probability · Mathematics 2018-10-10 Alessandra Faggionato , Hlafo Alfie Mimun

We study the performance of wireless links for a class of Poisson networks, in which packets arrive at the transmitters following Bernoulli processes. By combining stochastic geometry with queueing theory, two fundamental measures are…

Information Theory · Computer Science 2020-07-22 Howard H. Yang , Tony Q. S. Quek , H. Vincent Poor

In this letter, we introduce a general cellular network model where i) users and BSs are distributed as two general point processes that may be coupled, ii) pathloss is assumed to follow a multi-slope power-law pathloss model, and iii)…

Information Theory · Computer Science 2018-03-01 Mehrnaz Afshang , Chiranjib Saha , Harpreet S. Dhillon

In a large-scale wireless ad hoc network in which all transmitters form a homogeneous of Poisson point process, the statistics of the signal-to-interference ratio (SIR) in prior work is only derived in closed-form for the case of Rayleigh…

Information Theory · Computer Science 2015-05-27 Chun-Hung Liu

Percolation phenomena are pervasive in nature, ranging from capillary flow, crack propagation, ionic transport, fluid permeation, etc. Modeling percolation in highly-branched media requires the use of numerical solutions, as problems can…

Chemical Physics · Physics 2019-04-09 Asghar Aryanfar , William A. Goddard , Jaime Marian

We establish non-uniqueness regimes for the infinite-volume two-colored Widom--Rowlinson model based on inhomogeneous Poisson point processes with locally finite intensity measures featuring percolation. As an application, we provide…

Probability · Mathematics 2025-05-09 Benedikt Jahnel , Daniel Kamecke

The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…

Disordered Systems and Neural Networks · Physics 2015-05-19 R. A. da Costa , S. N. Dorogovtsev , A. V. Goltsev , J. F. F. Mendes

We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…

Probability · Mathematics 2025-10-29 Alessandra Faggionato , Ivailo Hartarsky