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Mathematics > Operator Algebras

arXiv:2210.02319 (math)
[Submitted on 5 Oct 2022 (v1), last revised 5 May 2023 (this version, v2)]

Title:Random amenable $\mathrm{C}^*$-algebras

Authors:Bhishan Jacelon
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Abstract:What is the probability that a random UHF algebra is of infinite type? What is the probability that a random simple AI algebra has at most $k$ extremal traces? What is the expected value of the radius of comparison of a random Villadsen-type AH algebra? What is the probability that such an algebra is $\mathcal{Z}$-stable? What is the probability that a random Cuntz-Krieger algebra is purely infinite and simple, and what can be said about the distribution of its $K$-theory? By constructing $\mathrm{C}^*$-algebras associated with suitable random (walks on) graphs, we provide context in which these are meaningful questions with computable answers.
Comments: This version of the article appears in the Mathematical Proceedings of the Cambridge Philosophical Society
Subjects: Operator Algebras (math.OA)
MSC classes: 46L05, 46L35, 60G50, 60J10, 05C80, 05C81
Cite as: arXiv:2210.02319 [math.OA]
  (or arXiv:2210.02319v2 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.2210.02319
Related DOI: https://doi.org/10.1017/S0305004123000178

Submission history

From: Bhishan Jacelon [view email]
[v1] Wed, 5 Oct 2022 15:20:00 UTC (23 KB)
[v2] Fri, 5 May 2023 14:05:36 UTC (22 KB)
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