0563793 20230418205210.320221109235959.9 85141487598 000910864400005 10.1214/22-EJP872 43 s. P cav_un_epca*00419541083-648927Institute of Mathematical Statistics frozen percolation recursive distributional equation recursive tree process endogeny 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 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0439738 Szőke M. HU 33 http://library.utia.cas.cz/separaty/2022/SI/swart-0563793.pdf https://dx.doi.org/10.1214/22-EJP872 GA20-08468S GA ČR cav_un_auth*0397552 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 i.i.d. 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. SCOPUS BA 10000 10100 10103 2023 3 RVO:67985556 https://hdl.handle.net/11104/0336405 S 145 3+4 Article Statistics Probability A STATISTICS&PROBABILITY 1.4 0.2 7.7 0.00798 1.375 2311 1.235 1.300 164 Q3 49.2 Q2 Q1 0.5 Q3 49.2 2022 85141487598 SCOPUS PUBMED 000910864400005 WOS cav_un_epca*0041954 Electronic Journal of Probability 1083-6489 1083-6489 Roč. 27 č. 1 2022 Institute of Mathematical Statistics