Operator K-theoretic analysis of random adjacency matrices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00636127" target="_blank" >RIV/67985840:_____/25:00636127 - isvavai.cz</a>

Výsledek na webu

<a href="https://nyjm.albany.edu/j/2025/31-28.html" target="_blank" >https://nyjm.albany.edu/j/2025/31-28.html</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Operator K-theoretic analysis of random adjacency matrices

Popis výsledku v původním jazyce

We appeal to results from combinatorial random matrix theory to deduce that various random graph C*-algebras are asymptotically almost surely Kirchberg algebras with trivial K1. This in particular implies that, with high probability, the stable isomorphism classes of such algebras are exhausted by variations of Cuntz algebras that we term 'Cuntz polygons'. These probabilistically generic algebras can be assembled into a Fraisse class whose limit structure G is consequently relevant to any K-theoretic analysis of finite graph C*-algebras. We also use computer simulations to experimentally verify the behaviour predicted by theory and to estimate the asymptotic probabilities of obtaining stable isomorphism classes represented by actual Cuntz algebras. These probabilities depend on the frequencies with which the Sylow p-subgroups of K0 are cyclic and in some cases can be computed from existing theory. For random symmetric r-regular multigraphs, current theory can describe these frequencies for finite sets of odd primes p not dividing r-1. A novel aspect of the collected data is the observation of new heuristics outside of this case, leading to a conjecture for the asymptotic probability of these graphs yielding C*-algebras stably isomorphic to Cuntz algebras. For other models of random multigraphs including Bernoulli (di)graphs, the data also allow us to estimate and heuristically explain the (surprisingly high) asymptotic probabilities of exact isomorphism to a Cuntz algebra. Recognising the role played by Cuntz-Krieger algebras in the theory of symbolic dynamics, we also collect supplemental data to estimate (and in some cases, actually compute) the asymptotic probability of a random subshift of finite type being flow equivalent to a full shift.

Název v anglickém jazyce

Operator K-theoretic analysis of random adjacency matrices

Popis výsledku anglicky

We appeal to results from combinatorial random matrix theory to deduce that various random graph C*-algebras are asymptotically almost surely Kirchberg algebras with trivial K1. This in particular implies that, with high probability, the stable isomorphism classes of such algebras are exhausted by variations of Cuntz algebras that we term 'Cuntz polygons'. These probabilistically generic algebras can be assembled into a Fraisse class whose limit structure G is consequently relevant to any K-theoretic analysis of finite graph C*-algebras. We also use computer simulations to experimentally verify the behaviour predicted by theory and to estimate the asymptotic probabilities of obtaining stable isomorphism classes represented by actual Cuntz algebras. These probabilities depend on the frequencies with which the Sylow p-subgroups of K0 are cyclic and in some cases can be computed from existing theory. For random symmetric r-regular multigraphs, current theory can describe these frequencies for finite sets of odd primes p not dividing r-1. A novel aspect of the collected data is the observation of new heuristics outside of this case, leading to a conjecture for the asymptotic probability of these graphs yielding C*-algebras stably isomorphic to Cuntz algebras. For other models of random multigraphs including Bernoulli (di)graphs, the data also allow us to estimate and heuristically explain the (surprisingly high) asymptotic probabilities of exact isomorphism to a Cuntz algebra. Recognising the role played by Cuntz-Krieger algebras in the theory of symbolic dynamics, we also collect supplemental data to estimate (and in some cases, actually compute) the asymptotic probability of a random subshift of finite type being flow equivalent to a full shift.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF22-07833K" target="_blank" >GF22-07833K: Homogenita a generičnost a metrických struktur - grup, dynamických systémů, Banachových prostorů a C*-algeber</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

New York Journal of Mathematics

ISSN

1076-9803

e-ISSN

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Svazek periodika

31

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

749-791

Kód UT WoS článku

001492728700001

EID výsledku v databázi Scopus

2-s2.0-105007469779