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

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 ${\mathrm{C}}^{\ast }$-algebras associated with suitable random (walks on) graphs, we provide context in which these are meaningful questions with computable answers.

This version of the article appears in the Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (2)

• The distribution of sandpile groups of random regular graphs
• Fraïssé limits of C*-algebras