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.

随机 UHF 代数为无限类型的概率是多少？随机简单 AI 代数最多具有k 条极值迹的概率是多少？随机 Villadsen 型 AH 代数的比较半径的期望值是多少？这样的代数$\mathcal{Z}$稳定的概率是多少？随机 Cuntz-Krieger 代数是纯粹无限且简单的概率是多少，其K理论的分布如何？通过构造与适当的随机（游走）图相关的$\mathrm{C}^*$代数，我们提供了上下文，其中这些是具有可计算答案的有意义的问题。