Frozen percolation on the binary tree is nonendogenous

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F21%3A00546728" target="_blank" >RIV/67985556:_____/21:00546728 - isvavai.cz</a>

Výsledek na webu

<a href="https://projecteuclid.org/journals/annals-of-probability/volume-49/issue-5/Frozen-percolation-on-the-binary-tree-is-nonendogenous/10.1214/21-AOP1507.short" target="_blank" >https://projecteuclid.org/journals/annals-of-probability/volume-49/issue-5/Frozen-percolation-on-the-binary-tree-is-nonendogenous/10.1214/21-AOP1507.short</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/21-AOP1507" target="_blank" >10.1214/21-AOP1507</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Frozen percolation on the binary tree is nonendogenous

Popis výsledku v původním jazyce

In frozen percolation, id. uniformly distributed activation times are assigned to the edges of a graph. At its assigned time an edge opens provided neither of its end vertices is part of an infinite open cluster, in the opposite case it freezes. Aldous (Math. Proc. Cambridge Philos. Soc. 128 (2000) 465–477) showed that such a process can be constructed on the infinite 3-regular tree and asked whether the event that a given edge freezes is a measurable function of the activation times assigned to all edges. We give a negative answer to this question, or, using an equivalent formulation and terminology introduced by Aldous and Bandyopadhyay (Ann. Appl. Probab. 15 (2005) 1047–1110), we show that the recursive tree process associated with frozen percolation on the oriented binary tree is nonendogenous. An essential role in our proofs is played by a frozen percolation process on a continuous-time binary Galton–Watson tree that has nice scale invariant properties.

Název v anglickém jazyce

Frozen percolation on the binary tree is nonendogenous

Popis výsledku anglicky

In frozen percolation, id. uniformly distributed activation times are assigned to the edges of a graph. At its assigned time an edge opens provided neither of its end vertices is part of an infinite open cluster, in the opposite case it freezes. Aldous (Math. Proc. Cambridge Philos. Soc. 128 (2000) 465–477) showed that such a process can be constructed on the infinite 3-regular tree and asked whether the event that a given edge freezes is a measurable function of the activation times assigned to all edges. We give a negative answer to this question, or, using an equivalent formulation and terminology introduced by Aldous and Bandyopadhyay (Ann. Appl. Probab. 15 (2005) 1047–1110), we show that the recursive tree process associated with frozen percolation on the oriented binary tree is nonendogenous. An essential role in our proofs is played by a frozen percolation process on a continuous-time binary Galton–Watson tree that has nice scale invariant properties.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastické evoluční rovnice a časoprostorové systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Annals of Probability

ISSN

0091-1798

e-ISSN

—

Svazek periodika

49

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

45

Strana od-do

2272-2316

Kód UT WoS článku

000700613800004

EID výsledku v databázi Scopus

2-s2.0-85117380337