Generating infinite random graphs
Csaba Bir\'o, Udayan B. Darji

TL;DR
This paper introduces a novel model for generating infinite random graphs based on a sequence of degrees, providing new characterizations and methods for constructing infinite random trees.
Contribution
It presents a new probabilistic model for infinite random graphs and trees, with a characterization and construction methods for such structures.
Findings
Provides a new characterization of infinite random graphs
Develops probabilistic methods for constructing infinite random trees
Analyzes the properties of the resulting probability space
Abstract
We define a growing model of random graphs. Given a sequence of nonnegative integers with the property that , we construct a random graph on countably infinitely many vertices by the following process: vertex is connected to a subset of of cardinality chosen uniformly at random. We study the resulting probability space. In particular, we give a new characterization of random graph and we also give probabilistic methods for constructing infinite random trees.
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