A limit theorem for small cliques in inhomogeneous random graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00543145" target="_blank" >RIV/67985807:_____/21:00543145 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985840:_____/21:00543145

Výsledek na webu

<a href="https://doi.org/10.1002/jgt.22673" target="_blank" >https://doi.org/10.1002/jgt.22673</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/jgt.22673" target="_blank" >10.1002/jgt.22673</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A limit theorem for small cliques in inhomogeneous random graphs

Popis výsledku v původním jazyce

The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erdős-Rényi random graph, called W-random graphs. We prove, via the method of moments, a limit theorem for the number of r-cliques in such random graphs. We show that, whereas in the case of dense Erdős-Rényi random graphs the fluctuations are normal of order n^{r-1}, the fluctuations in the setting of W-random graphs may be of order 0, n^{r-1}, or n^{r-0.5}. Furthermore, when the fluctuations are of order n^{r-0.5} they are normal, while when the fluctuations are of order n^{r-1} they exhibit either normal or a particular type of chi-square behavior whose parameters relate to spectral properties of W. These results can also be deduced from a general setting, based on the projection method. In addition to providing alternative proofs, our approach makes direct links to the theory of graphons.

Název v anglickém jazyce

A limit theorem for small cliques in inhomogeneous random graphs

Popis výsledku anglicky

The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erdős-Rényi random graph, called W-random graphs. We prove, via the method of moments, a limit theorem for the number of r-cliques in such random graphs. We show that, whereas in the case of dense Erdős-Rényi random graphs the fluctuations are normal of order n^{r-1}, the fluctuations in the setting of W-random graphs may be of order 0, n^{r-1}, or n^{r-0.5}. Furthermore, when the fluctuations are of order n^{r-0.5} they are normal, while when the fluctuations are of order n^{r-1} they exhibit either normal or a particular type of chi-square behavior whose parameters relate to spectral properties of W. These results can also be deduced from a general setting, based on the projection method. In addition to providing alternative proofs, our approach makes direct links to the theory of graphons.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of Graph Theory

ISSN

0364-9024

e-ISSN

1097-0118

Svazek periodika

97

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

578-599

Kód UT WoS článku

000633807200001

EID výsledku v databázi Scopus

2-s2.0-85103206459