Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Random quantum graphs
HTML articles powered by AMS MathViewer

by Alexandru Chirvasitu and Mateusz Wasilewski PDF
Trans. Amer. Math. Soc. 375 (2022), 3061-3087 Request permission

Abstract:

We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,\cdots ,X_d)$ of traceless self-adjoint operators in the $n\times n$ matrix algebra the corresponding operator system has trivial automorphism group, in the largest possible range for the parameters: $2\le d\le n^2-3$. Moreover, the automorphism group is generically abelian in the larger parameter range $1\le d\le n^2-2$. This then implies that for those respective parameters the corresponding random-quantum-graph model built on the GUE ensembles of $X_i$’s (mimicking the Erdős-Rényi $G(n,p)$ model) has trivial/abelian automorphism group almost surely.
References
Similar Articles
Additional Information
  • Alexandru Chirvasitu
  • Affiliation: Department of Mathematics, University at Buffalo, Buffalo, New York 14260-2900
  • MR Author ID: 868724
  • Email: achirvas@buffalo.edu
  • Mateusz Wasilewski
  • Affiliation: Department of Mathematics – Section of Analysis, KU Leuven, Leuven, Belgium
  • Address at time of publication: Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
  • MR Author ID: 1146862
  • ORCID: 0000-0002-3952-777X
  • Email: mwasilewski@impan.pl
  • Received by editor(s): December 19, 2020
  • Received by editor(s) in revised form: March 29, 2021, and May 24, 2021
  • Published electronically: February 9, 2022
  • Additional Notes: The first author is grateful for funding through NSF grant DMS-2001128. The second author was supported by the Research Foundation—Flanders (FWO) through a Postdoctoral Fellowship and by long term structural funding—Methusalem grant of the Flemish Government
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 3061-3087
  • MSC (2020): Primary 60B20, 05C80, 20G20, 20B25, 22E45, 15A30
  • DOI: https://doi.org/10.1090/tran/8584
  • MathSciNet review: 4402656