Frozen percolation on the binary tree is nonendogenous
| Autor: | Balázs Ráth, Jan M. Swart, Tamás Terpai |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
82C27 (Primary) 60K35 82C26 60J80 (Secondary) Binary tree Measurable function Probability (math.PR) Binary number Recursive tree Combinatorics Mathematics::Probability Percolation FOS: Mathematics Tree (set theory) Statistics Probability and Uncertainty Mathematics - Probability Branching process Event (probability theory) Mathematics |
| Popis: | 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 endvertices is part of an infinite open cluster; in the opposite case, it freezes. Aldous (2000) 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 (2005), 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. 45 pages, 3 figures. Minor corrections compared to the first and second versions |
| Databáze: | OpenAIRE |
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