Short Talk: Jose Chacon Martinez

Exchangeable fast fragmentation-coalescence (EFFC) processes are partition-valued processes on P(N) that combine a coalescence mechanism with an extreme form of fragmentation that drives the number of blocks to infinity. In our current research, we investigate the property of coming down from infinity (CDFI), which refers to the ability of the associated block counting process to become finite instantaneously, even when starting from an infinite number of blocks. We approach this through extensions of classic techniques from coalescence theory, such as the look-down construction and duality with forward-in-time frequency processes, among others. In particular, for 0 < alpha < 1, we establish a novel threshold for CDFI in the EFFC process arising from the combination of a Beta(alpha, 2 - alpha)-coalescent with a class of extreme fragmentation mechanisms.