Deviation probabilities for arithmetic progressions and irregular discrete structures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00581051" target="_blank" >RIV/67985807:_____/23:00581051 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1214/23-EJP1012" target="_blank" >https://doi.org/10.1214/23-EJP1012</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/23-EJP1012" target="_blank" >10.1214/23-EJP1012</a>

Result language
angličtina
Original language name
Deviation probabilities for arithmetic progressions and irregular discrete structures
Original language description
Let the random variable X:=e(H[B]) count the number of edges of a hypergraph H induced by a random m-element subset B of its vertex set. Focussing on the case that the degrees of vertices in H vary significantly we prove bounds on the probability that X is far from its mean. It is possible to apply these results to discrete structures such as the set of k-term arithmetic progressions in {1,…,N}. Furthermore, our main theorem allows us to deduce results for the case B∼Bp is generated by including each vertex independently with probability p. In this setting our result on arithmetic progressions extends a result of Bhattacharya, Ganguly, Shao and Zhao [5]. We also mention connections to related central limit theorems.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ20-27757Y" target="_blank" >GJ20-27757Y: Random discrete structures</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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