A phase transition between endogeny and nonendogeny

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F22%3A00563793" target="_blank" >RIV/67985556:_____/22:00563793 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.1214/22-EJP872" target="_blank" >https://dx.doi.org/10.1214/22-EJP872</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1214/22-EJP872" target="_blank" >10.1214/22-EJP872</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A phase transition between endogeny and nonendogeny

Popis výsledku v původním jazyce

The Marked Binary Branching Tree (MBBT) is the family tree of a rate one binary branching process, on which points have been generated according to a rate one Poisson point process, with id. uniformly distributed activation times assigned to the points. In frozen percolation on the MBBT, initially, all points are closed, but as time progresses points can become either frozen or open. Points become open at their activation times provided they have not become frozen before. Open points connect the parts of the tree below and above it and one says that a point percolates if the tree above it is infinite. We consider a version of frozen percolation on the MBBT in which at times of the form θ^n, all points that percolate are frozen. The limiting model for θ → 1, in which points freeze as soon as they percolate, has been studied before by Ráth, Swart, and Terpai. We extend their results by showing that there exists a 0 < θ∗ < 1 such that the model is endogenous for θ ≤ θ∗ but not for θ > θ∗. This means that for θ ≤ θ∗, frozen percolation is a.s. determined by the MBBT but for θ∗ > θ one needs additional randomness to describe it.

Název v anglickém jazyce

A phase transition between endogeny and nonendogeny

Popis výsledku anglicky

The Marked Binary Branching Tree (MBBT) is the family tree of a rate one binary branching process, on which points have been generated according to a rate one Poisson point process, with id. uniformly distributed activation times assigned to the points. In frozen percolation on the MBBT, initially, all points are closed, but as time progresses points can become either frozen or open. Points become open at their activation times provided they have not become frozen before. Open points connect the parts of the tree below and above it and one says that a point percolates if the tree above it is infinite. We consider a version of frozen percolation on the MBBT in which at times of the form θ^n, all points that percolate are frozen. The limiting model for θ → 1, in which points freeze as soon as they percolate, has been studied before by Ráth, Swart, and Terpai. We extend their results by showing that there exists a 0 < θ∗ < 1 such that the model is endogenous for θ ≤ θ∗ but not for θ > θ∗. This means that for θ ≤ θ∗, frozen percolation is a.s. determined by the MBBT but for θ∗ > θ one needs additional randomness to describe it.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA20-08468S" target="_blank" >GA20-08468S: Limity interagujících stochastických modelů na velkých škálách</a><br>

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

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

1083-6489

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

145

Kód UT WoS článku

000910864400005

EID výsledku v databázi Scopus

2-s2.0-85141487598