The structure of random automorphisms of the random graph

2018/08/18 by Udayan B. Darji, Darji, Udayan B., Márton Elekes +7
Biochemistry, Genetics and Molecular Biology · #FOS: Mathematics #Genetic Syndromes and Imprinting #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1808.06121

openalex publication_date 2018/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete description of the size of the conjugacy classes of the automorphism group of the random graph with respect to Christensen's Haar null ideal. It is shown that every non-Haar null class contains a translated copy of a nonempty portion of every compact set and that there are continuum many non-Haar null conjugacy classes. Our methods also yield a new proof of an old result of Truss.

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