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A phase transition in the coming down fr...
Foucart, Clément...

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A phase transition in the coming down from infinity of simple exchangeable fragmentation-coagulation processes by Foucart, Clément ( Author )
Lemonjar Open Access
Australian National University
08-08-2023
We consider the class of exchangeable fragmentation-coagulation (EFC) processes where coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and fragmentation dislocates at finite rate an individual block into sub-blocks of infinite size. We call these partition-valued processes, simple EFC processes, and study the question whether such a process, when started with infinitely many blocks, can visit partitions with a finite number of blocks or not. When this occurs, one says that the process comes down from infinity. We introduce two sharp parameters $\theta_{\star}\leq \theta^{\star}\in [0,\infty]$, so that if $\theta^{\star}<1$, the process comes down from infinity and if $\theta_\star>1$, then it stays infinite. We illustrate our result with regularly varying coagulation and fragmentation measures. In this case, the parameters $\theta_{\star},\theta^{\star}$ coincide and are explicit.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1605.07039
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