# Boundary Behaviors at $\infty$ for Fragments in Simple Exchangeable Fragmentation-Coalescence Processes

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### ：Xiaowen Zhou：2021-08-27 08:00：腾讯会议 ID： 947 842 339（无密码）

间：202182708:00

点：腾讯会议 ID 947 842 339（无密码）

Exchangeable fragmentation-coagulation (EFC) processes are partition-valued stochastic processes first introduced by Berestycki. In this talk we consider the EFC processes for which the coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and the fragmentations dislocate at finite rate an individual block into sub-blocks of infinite size. Sufficient conditions are found for the block counting process to explode (i.e. to reach $\infty$) or not and for $\infty$ to be either an exit boundary or an entrance boundary. In a case of regularly varying fragmentation and coagulation mechanisms, we find regimes where the boundary $\infty$ can be either an exit, an entrance or a regular boundary. (This talk is based on joint work with Clement Foucart.)