A limit theorem for small cliques in inhomogeneous random graphs
The result's identifiers
Result code in 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>
Alternative codes found
RIV/67985840:_____/21:00543145
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A limit theorem for small cliques in inhomogeneous random graphs
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Graph Theory
ISSN
0364-9024
e-ISSN
1097-0118
Volume of the periodical
97
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
22
Pages from-to
578-599
UT code for WoS article
000633807200001
EID of the result in the Scopus database
2-s2.0-85103206459