Adrien Gonzales Casanova

We define a new class of $\Xi$-coalescents characterized by a possibly infinite measure over the non-negative integers. We call them symmetric coalescents since they are the unique family of exchangeable coalescents satisfying a symmetry property on their coagulation rates: they are invariant under any transformation that consists in moving one element from one block to another without changing the total number of blocks. We illustrate the diversity of behaviours of this family of processes by introducing and studying a one parameter subclass, the $(\beta,S)$-coalescents.