On the upper tail of star counts in random graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00635806" target="_blank" >RIV/67985807:_____/25:00635806 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1214/25-EJP1345" target="_blank" >https://doi.org/10.1214/25-EJP1345</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/25-EJP1345" target="_blank" >10.1214/25-EJP1345</a>
Alternative languages
Result language
angličtina
Original language name
On the upper tail of star counts in random graphs
Original language description
Let X count the number of r-stars in the random binomial graph G (n,p). We determine, for fixed r and ε > 0, the asymptotics of log P (X ≥ (1 + ε)EX) assuming only EX→∞ and p→0 thus giving a first class of irregular graphs for which the upper tail problem for subgraph counts (stated by Janson and Ruciński in 2004) is solved in the sparse setting.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Probability
ISSN
1083-6489
e-ISSN
1083-6489
Volume of the periodical
30
Issue of the periodical within the volume
2025
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
82
UT code for WoS article
001540927000002
EID of the result in the Scopus database
2-s2.0-105007166892