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
![]() |
PDF
- Accepted Version
See Usage Policy. 842kB |
![]() |
PDF
- Submitted Version
See Usage Policy. 394kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20220607-425364000
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: |
| ||||||||||
ORCID: |
| ||||||||||
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: |
| ||||||||||
Subject Keywords: | Non-locally compact Polish group; Haar null; Typical element; Automorphism group; Random automorphism; Random graph | ||||||||||
Issue or Number: | 9 | ||||||||||
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 |
Repository Staff Only: item control page