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Topological Properties of an Exponential Random Geometric Graph Process
Authors: Yilun Shang
Abstract:In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062986Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1116
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