TL;DR
This paper introduces a new construction for generating geometric finite random graphs, exploring their connections to advanced probabilistic concepts like the Poisson boundary and random interlacements.
Contribution
It presents a novel method for constructing geometric random graphs and links these structures to key probabilistic theories and boundaries.
Findings
Establishes connections between geometric random graphs and Poisson boundary.
Links Naim's kernel to the structure of these graphs.
Relates the graphs to Sznitman's random interlacements.
Abstract
We introduce a construction that gives rise to a variety of "geometric" finite random graphs, and describe connections to the Poisson boundary, Naim's kernel, and Sznitman's random interlacements.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Geometric and Algebraic Topology