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In this paper, we study the performance of non-fading and Rayleigh fading ad hoc networks. We first characterize the distribution of the signal-to-interference-plus-noise ratio (SINR) through the Laplace transform of the inverted SINR for…

Information Theory · Computer Science 2015-09-15 Hieu Duy Nguyen , Sumei Sun

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized…

Probability · Mathematics 2016-02-01 Christophe Sabot , Laurent Tournier

We define natural probability measures on cycle-rooted spanning forests (CRSFs) on graphs embedded on a surface with a Riemannian metric. These measures arise from the Laplacian determinant and depend on the choice of a unitary connection…

Probability · Mathematics 2017-04-06 Adrien Kassel , Richard Kenyon

Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to \mathbb{R}^k$, that we interpret as random variables with…

Differential Geometry · Mathematics 2021-01-25 Antonio Lerario , Michele Stecconi

Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…

Probability · Mathematics 2010-08-31 Laurent Decreusefond , Eduardo Ferraz

We study random walk among random conductance (RWRC) on complete graphs with N vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution…

Probability · Mathematics 2018-09-20 Andrea Collevecchio , Paul Jung

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…

Quantitative Methods · Quantitative Biology 2017-02-07 John Lang , Hans De Sterck , Jamieson L. Kaiser , Joel C. Miller

Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions…

Information Theory · Computer Science 2012-04-12 Dionissios T. Hristopulos , Samuel Elogne

Strongly Rayleigh distributions are a class of negatively dependent distributions of binary-valued random variables [Borcea, Branden, Liggett JAMS 09]. Recently, these distributions have played a crucial role in the analysis of algorithms…

Probability · Mathematics 2018-10-22 Rasmus Kyng , Zhao Song

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter…

Machine Learning · Statistics 2015-05-20 Wesley Tansey , Oscar Hernan Madrid Padilla , Arun Sai Suggala , Pradeep Ravikumar

We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…

Probability · Mathematics 2018-06-29 Frank Aurzada , Sebastian Schwinn

Random dynamical systems (RDS) evolve by a dynamical rule chosen independently with a certain probability, from a given set of deterministic rules. These dynamical systems in an interval reach a steady state with a unique well-defined…

Statistical Mechanics · Physics 2020-09-21 M. S. Shesha Gopal , Soumitro Banerjee , P. K. Mohanty

Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been limited to discrete domains due to their…

Machine Learning · Computer Science 2021-10-20 Yuqiao Chen , Sriraam Natarajan , Nicholas Ruozzi

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

Probability · Mathematics 2021-11-24 N. H. Bingham , Tasmin L. Symons

Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the…

Statistical Mechanics · Physics 2024-10-16 Luca Angelani , Alessandro De Gregorio , Roberto Garra , Francesco Iafrate

We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…

Probability · Mathematics 2019-04-09 Krzysztof Bisewski , Daan Crommelin , Michel Mandjes

Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…

Machine Learning · Computer Science 2026-02-03 Sawan Kumar , Souvik Chakraborty

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…

Probability · Mathematics 2022-10-10 Alexandre Boyer , Jérôme Casse , Nathanaël Enriquez , Arvind Singh

We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…

Probability · Mathematics 2015-01-14 Masato Shinoda , Elmar Teufl , Stephan Wagner

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

Classical Physics · Physics 2007-05-23 S. Tim Hatamian