English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We appeal to results from combinatorial random matrix theory to deduce thatvarious random graph $\mathrm{C}^*$-algebras are asymptotically almost surelyKirchberg algebras with trivial $K_1$. This in particular implies that, withhigh probability, the stable isomorphism classes of such algebras are exhaustedby variations of Cuntz algebras that we term 'Cuntz polygons'. We also usecomputer simulations to experimentally verify the behaviour predicted by theoryand to estimate the asymptotic probabilities of obtaining stable isomorphismclasses represented by actual Cuntz algebras. These probabilities depend on thefrequencies with which the Sylow $p$-subgroups of $K_0$ are cyclic. For randomsymmetric $r$-regular multigraphs, current theory can describe thesefrequencies for finite sets of odd primes $p$ not dividing $r-1$. A novelaspect of the collected data is the observation of new heuristics outside ofthis case, leading to a conjecture for the asymptotic probability of thesegraphs yielding $\mathrm{C}^*$-algebras stably isomorphic to Cuntz algebras.

The $K$-distribution of random graph $\mathrm{C}^*$-algebras