2015/01/07 by Erich Baur, Baur, Erich, Jean Bertoin +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1501.01400
openalex publication_date 2015/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a natural destruction process of an infinite recursive tree by\nremoving each edge after an independent exponential time. The destruction up to\ntime t is encoded by a partition \Π(t) of N into blocks of connected\nvertices. Despite the lack of exchangeability, just like for an exchangeable\nfragmentation process, the process \Π is Markovian with transitions\ndetermined by a splitting rates measure r. However, somewhat surprisingly, r\nfails to fulfill the usual integrability condition for the dislocation measure\nof exchangeable fragmentations. We further observe that a time-dependent\nnormalization enables us to define the weights of the blocks of \Π(t). We\nstudy the process of these weights and point at connections with\nOrnstein-Uhlenbeck type processes.\n