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arXiv · 2210.02319

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

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.

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Bhishan Jacelon. 2022-10-05. Random amenable $\mathrm{C}^*$-algebras. https://doi.org/10.1017/s0305004123000178

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