Relating the cut distance and the weak* topology for graphons

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00536782" target="_blank" >RIV/67985807:_____/21:00536782 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985840:_____/21:00536782

Výsledek na webu

<a href="https://doi.org/10.1016/j.jctb.2020.04.003" target="_blank" >https://doi.org/10.1016/j.jctb.2020.04.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jctb.2020.04.003" target="_blank" >10.1016/j.jctb.2020.04.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relating the cut distance and the weak* topology for graphons

Popis výsledku v původním jazyce

The theory of graphons is ultimately connected with the so-called cut norm. In this paper, we approach the cut norm topology via the weak* topology (when considering a predual of L1-functions). We prove that a sequence W1, W2, W3, ... of graphons converges in the cut distance if and only if we have equality of the sets of weak* accumulation points and of weak* limit points of all sequences of graphons W1, W2, W3, ... that are weakly isomorphic to W1, W2, W3, ... . We further give a short descriptive set theoretic argument that each sequence of graphons contains a subsequence with the property above. This in particular provides an alternative proof of the theorem of Lovász and Szegedy about compactness of the space of graphons. We connect these results to 'multiway cut' characterization of cut distance convergence from [Ann. of Math. (2) 176 (2012), no. 1, 151-219]. These results are more naturally phrased in the Vietoris hyperspace K over graphons with the weak* topology.

Název v anglickém jazyce

Relating the cut distance and the weak* topology for graphons

Popis výsledku anglicky

The theory of graphons is ultimately connected with the so-called cut norm. In this paper, we approach the cut norm topology via the weak* topology (when considering a predual of L1-functions). We prove that a sequence W1, W2, W3, ... of graphons converges in the cut distance if and only if we have equality of the sets of weak* accumulation points and of weak* limit points of all sequences of graphons W1, W2, W3, ... that are weakly isomorphic to W1, W2, W3, ... . We further give a short descriptive set theoretic argument that each sequence of graphons contains a subsequence with the property above. This in particular provides an alternative proof of the theorem of Lovász and Szegedy about compactness of the space of graphons. We connect these results to 'multiway cut' characterization of cut distance convergence from [Ann. of Math. (2) 176 (2012), no. 1, 151-219]. These results are more naturally phrased in the Vietoris hyperspace K over graphons with the weak* topology.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of Combinatorial Theory. B

ISSN

0095-8956

e-ISSN

1096-0902

Svazek periodika

147

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

47

Strana od-do

252-298

Kód UT WoS článku

000605462900011

EID výsledku v databázi Scopus

2-s2.0-85084518436