0546728 20250310155914.420211015235959.9 85117380337 000700613800004 10.1214/21-AOP1507 45 s. P cav_un_epca*02508150091-1798495 (2021)2272-2316Institute of Mathematical Statistics frozen percolation self-organised criticality recursive distributional equation recursive tree process endogeny near-critical percolation branching process cav_un_auth*0415461 Ráth B. HU 34 cav_un_auth*0217893 Swart Jan M. UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics CZ 33 K Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0415462 Terpai T. HU 33 http://library.utia.cas.cz/separaty/2021/SI/swart-0546728.pdf https://projecteuclid.org/journals/annals-of-probability/volume-49/issue-5/Frozen-percolation-on-the-binary-tree-is-nonendogenous/10.1214/21-AOP1507.short GA19-07140S GA ČR CZ cav_un_auth*0385132 In frozen percolation, i.i.d. 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. WOS BA 10000 10100 10103 2022 3 2 R hod 4 4rh 4 20250310155444.9 4 20250310155914.4 RVO:67985556 http://hdl.handle.net/11104/0323442 cav_un_auth*0320137 Budapest University of Technology and Economics BME HU cav_un_auth*0415463 Eötvös Loránd University ELTE HU S 3+4 Article Statistics Probability C STATISTICS&PROBABILITY 2.624 0.494 18.2 0.01235 2.718 6976 105 2.955 37.04 2.32 628 Q1 2.063 79 Q2 72.4 Q1 Q1* 1.06 Q1 72.4 2021 Soubory v repozitáři: swart-0546728.pdf 85117380337 SCOPUS PUBMED 000700613800004 WOS cav_un_epca*0250815 Annals of Probability 0091-1798 Roč. 49 č. 5 2021 2272 2316 Institute of Mathematical Statistics