Scaling limits of branching random walks and branching stable processes

Jean Bertoin, Hairuo Yang

Published 2021-03-12Version 1

Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their do- mains of attraction and describe explicit conditions for a branching random walk to converge after a proper magnification to a branching-stable process. This contrasts with deep results that have been obtained during the last decade on the asymptotic behavior of branching random walks and which involve either shifting without rescaling, or demagnification.