The structure of random automorphisms of the random graph

Darji, U.B. and Elekes, Márton and Kalina, K. and Kiss, Viktor and Vidnyánszky, Zoltán (2022) The structure of random automorphisms of the random graph. ANNALS OF PURE AND APPLIED LOGIC, 173 (9). ISSN 0168-0072

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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. © 2022

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