Published October 2022
| Submitted
Journal Article
Open
The structure of random automorphisms of the random graph
Chicago
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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.
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.Attached Files
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Additional details
- Eprint ID
- 115062
- DOI
- 10.1016/j.apal.2022.103152
- Resolver ID
- CaltechAUTHORS:20220607-425364000
- 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
- Created
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2022-06-07Created from EPrint's datestamp field
- Updated
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2022-07-15Created from EPrint's last_modified field