The structure of random automorphisms of the random graph

Darji, Udayan B. and Elekes, Márton and Kalina, Kende and Kiss, Viktor and Vidnyánszky, Zoltán (2022) The structure of random automorphisms of the random graph. Annals of Pure and Applied Logic, 173 (9). Art. No. 103152. ISSN 0168-0072. doi:10.1016/j.apal.2022.103152. https://resolver.caltech.edu/CaltechAUTHORS:20220607-425364000

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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.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1016/j.apal.2022.103152	DOI	Article
https://arxiv.org/abs/1808.06121	arXiv	Discussion Paper

ORCID:

Author	ORCID
Vidnyánszky, Zoltán	0000-0001-8168-9353

Additional Information:

© 2022 Published by Elsevier. Received 5 November 2021, Revised 29 May 2022, Accepted 1 June 2022, Available online 3 June 2022. The second, fourth and fifth authors were partially supported by the National Research, Development and Innovation Office – NKFIH, grants no. 113047, no. 104178 and no. 124749. The fifth author was also supported by FWF Grant P29999. We would like to thank to R. Balka, Z. Gyenis, A. Kechris, C. Rosendal, S. Solecki and P. Wesolek for many valuable remarks and discussions. We are also very grateful to the anonymous referee for numerous valuable suggestions.

Funders:

Funding Agency	Grant Number
National Research, Development and Innovation Fund (NKFIA)	113047
National Research, Development and Innovation Fund (NKFIA)	104178
National Research, Development and Innovation Fund (NKFIA)	124749
FWF Der Wissenschaftsfonds	P29999

Subject Keywords:

Non-locally compact Polish group; Haar null; Typical element; Automorphism group; Random automorphism; Random graph

Issue or Number:

Classification Code:

MSC: primary 03E15; 22F50; secondary 03C15; 28A05; 54H11; 28A99

DOI:

10.1016/j.apal.2022.103152

Record Number:

CaltechAUTHORS:20220607-425364000

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20220607-425364000

Official Citation:

Udayan B. Darji, Márton Elekes, Kende Kalina, Viktor Kiss, Zoltán Vidnyánszky, The structure of random automorphisms of the random graph, Annals of Pure and Applied Logic, Volume 173, Issue 9, 2022, 103152, ISSN 0168-0072, https://doi.org/10.1016/j.apal.2022.103152.

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

115062

Collection:

CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

07 Jun 2022 20:14

Last Modified:

15 Jul 2022 19:39

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