Frozen percolation on the binary tree is nonendogenous
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Frozen percolation on the binary tree is nonendogenous
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA19-07140S" target="_blank" >GA19-07140S: Stochastic Evolution Equations and Space-Time Systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Probability
ISSN
0091-1798
e-ISSN
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Volume of the periodical
49
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
45
Pages from-to
2272-2316
UT code for WoS article
000700613800004
EID of the result in the Scopus database
2-s2.0-85117380337