Deviation probabilities for arithmetic progressions and irregular discrete structures

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Deviation probabilities for arithmetic progressions and irregular discrete structures

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Deviation probabilities for arithmetic progressions and irregular discrete structures

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-27757Y" target="_blank" >GJ20-27757Y: Náhodné diskrétní struktury</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

1083-6489

Svazek periodika

28

Číslo periodika v rámci svazku

2023

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

172 (s. 1-31)

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85183172344