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We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

Disordered Systems and Neural Networks · Physics 2015-05-13 A. C. C. Coolen , A. De Martino , A. Annibale

We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…

Data Structures and Algorithms · Computer Science 2020-01-03 Ce Jin

Consider a random regular graph of fixed degree $d$ with $n$ vertices. We study spectral properties of the adjacency matrix and of random Schr\"odinger operators on such a graph as $n$ tends to infinity. We prove that the integrated density…

Mathematical Physics · Physics 2014-05-09 Leander Geisinger

An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…

Disordered Systems and Neural Networks · Physics 2009-11-13 Paul E. Parris , Julián Candia , V. M. Kenkre

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

Probability · Mathematics 2021-12-07 Ágnes Backhausz , Charles Bordenave , Balázs Szegedy

We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…

Discrete Mathematics · Computer Science 2023-08-22 Alexander Cloninger , Gal Mishne , Andreas Oslandsbotn , Sawyer Jack Robertson , Zhengchao Wan , Yusu Wang

We consider two random walks evolving synchronously on a random out-regular graph of $n$ vertices with bounded out-degree $r\ge 2$, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with…

Probability · Mathematics 2023-11-30 Matteo Quattropani , Federico Sau

For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…

Probability · Mathematics 2017-11-06 Matthias Reitzner , Matthias Schulte , Christoph Thaele

Random walk based distributed algorithms make use of a token that circulates in the system according to a random walk scheme to achieve their goal. To study their efficiency and compare it to one of the deterministic solutions, one is led…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-07-24 Alain Bui , Devan Sohier

In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…

Data Analysis, Statistics and Probability · Physics 2011-07-05 Kye M. Taylor , Francois G. Meyer

We investigate random processes for generating task-dependency graphs of order $n$ with $m$ edges and a specified number of initial vertices and terminal vertices. In order to do so, we consider two random processes for generating…

Discrete Mathematics · Computer Science 2023-05-10 Jesse Geneson , Shen-Fu Tsai

Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…

Discrete Mathematics · Computer Science 2018-11-05 Varun Kanade , Frederik Mallmann-Trenn , Thomas Sauerwald

We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…

Probability · Mathematics 2011-10-27 Ron Rosenthal

We study the problem of collaboratively estimating the state of a discrete-time LTI process by a network of sensor nodes interacting over a time-varying directed communication graph. Existing approaches to this problem either (i) make…

Systems and Control · Computer Science 2018-10-16 Aritra Mitra , John A. Richards , Saurabh Bagchi , Shreyas Sundaram

The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…

Probability · Mathematics 2026-04-16 Luca Avena , Gianmarco Bet , Lars Schroeder , Clara Stegehuis

For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks…

Probability · Mathematics 2018-12-04 Amir Dembo , Ruojun Huang , Tianyi Zheng

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the non-ergodic phase, the…

Statistical Mechanics · Physics 2015-06-24 Johannes H. P. Schulz , Eli Barkai

Inspired by the study of edge statistics of random band matrices, we investigate random walks on large $d$-dimensional periodic lattices, whose transition matrices are determined by discretized density functions. Under certain moment…

Probability · Mathematics 2024-11-07 Yandong Gu , Dang-Zheng Liu

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…

Social and Information Networks · Computer Science 2018-05-02 Xiao Zhang , Cristopher Moore , M. E. J. Newman

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

Optimization and Control · Mathematics 2016-09-20 Damjan Škulj