Cut distance identifying graphon parameters over weak* limits

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00556339" target="_blank" >RIV/67985807:_____/22:00556339 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985840:_____/22:00556339

Výsledek na webu

<a href="https://doi.org/10.1016/j.jcta.2022.105615" target="_blank" >https://doi.org/10.1016/j.jcta.2022.105615</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcta.2022.105615" target="_blank" >10.1016/j.jcta.2022.105615</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cut distance identifying graphon parameters over weak* limits

Popis výsledku v původním jazyce

The theory of graphons comes with the so-called cut norm and the derived cut distance. The cut norm is finer than the weak* topology (when considering the predual of L1-functions). Doležal and Hladký ((2019) [13]) showed, that given a sequence of graphons, a cut distance accumulation graphon can be pinpointed in the set of weak* accumulation points as a minimizer of the entropy. Motivated by this, we study graphon parameters with the property that their minimizers or maximizers identify cut distance accumulation points over the set of weak* accumulation points. We call such parameters cut distance identifying. Of particular importance are cut distance identifying parameters coming from homomorphism densities, t(H,⋅). This concept is closely related to the emerging field of graph norms, and the notions of the step Sidorenko property and the step forcing property introduced by Král', Martins, Pach and Wrochna ((2019) [25]). We prove that a connected graph is weakly norming if and only if it is step Sidorenko, and that if a graph is norming then it is step forcing. Further, we study convexity properties of cut distance identifying graphon parameters, and find a way to identify cut distance limits using spectra of graphons. We also show that continuous cut distance identifying graphon parameters have the <[removed]>, and thus can be used in the proof of the Frieze–Kannan regularity lemma.

Název v anglickém jazyce

Cut distance identifying graphon parameters over weak* limits

Popis výsledku anglicky

The theory of graphons comes with the so-called cut norm and the derived cut distance. The cut norm is finer than the weak* topology (when considering the predual of L1-functions). Doležal and Hladký ((2019) [13]) showed, that given a sequence of graphons, a cut distance accumulation graphon can be pinpointed in the set of weak* accumulation points as a minimizer of the entropy. Motivated by this, we study graphon parameters with the property that their minimizers or maximizers identify cut distance accumulation points over the set of weak* accumulation points. We call such parameters cut distance identifying. Of particular importance are cut distance identifying parameters coming from homomorphism densities, t(H,⋅). This concept is closely related to the emerging field of graph norms, and the notions of the step Sidorenko property and the step forcing property introduced by Král', Martins, Pach and Wrochna ((2019) [25]). We prove that a connected graph is weakly norming if and only if it is step Sidorenko, and that if a graph is norming then it is step forcing. Further, we study convexity properties of cut distance identifying graphon parameters, and find a way to identify cut distance limits using spectra of graphons. We also show that continuous cut distance identifying graphon parameters have the <[removed]>, and thus can be used in the proof of the Frieze–Kannan regularity lemma.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. A

ISSN

0097-3165

e-ISSN

1096-0899

Svazek periodika

189

Číslo periodika v rámci svazku

July

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

57

Strana od-do

105615

Kód UT WoS článku

000793602100001

EID výsledku v databázi Scopus

2-s2.0-85126595545