Upper Tail Bounds for Stars

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00523427" target="_blank" >RIV/67985807:_____/20:00523427 - isvavai.cz</a>
Result on the web
<a href="http://hdl.handle.net/11104/0307782" target="_blank" >http://hdl.handle.net/11104/0307782</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/8493" target="_blank" >10.37236/8493</a>

Result language
angličtina
Original language name
Upper Tail Bounds for Stars
Original language description
For r ≥ 2, let X be the number of r-armed stars K_{1,r} in the binomial random graph G(n,p). We study the upper tail P(X ≥ (1+ε)EX), and establish exponential bounds which are best possible up to constant factors in the exponent (for the special case of stars K_{1,r} this solves a problem of Janson and Ruciński, and confirms a conjecture by DeMarco and Kahn). In contrast to the widely accepted standard for the upper tail problem, we do not restrict our attention to constant ε, but also allow for ε ≥ n^(-a) deviations.
Czech name
—
Czech description
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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

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

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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