Conditionally Poissonian random digraphs

Christian Mönch

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arXiv · 1705.03801

Conditionally Poissonian random digraphs

Christian Mönch

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Abstract

We define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced by Norros and Reittu in Adv. Appl. Probab. 38 (2006), 59--75. Its loopless simple projection is a rank-one independent-arc inhomogeneous digraph of the type studied by Cao and Olvera-Cravioto, Random Struct. Alg. 56 (2020), 722--774. For the Poissonian multigraph itself, we discuss the relation to Norros-Reittu graphs, characterise limiting degree distributions, and record explicit exploration estimates. In particular, we give fixed-depth directed local weak limits, stopped branching-process couplings with weight-mass collision budgets, a comparison with the simple projection, and a rare-event concentration criterion. These estimates are intended as graph-side structural inputs for later dynamics on the graph.

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BibTeX RIS

Christian Mönch. 2017-05-10. Conditionally Poissonian random digraphs. https://arxiv.org/abs/1705.03801

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