Reinforced Galton–Watson processes II: Large time behaviors

Reinforced Galton–Watson processes have been introduced in (Random Structures Algorithms 65 (2024) 387–410) as population models with nonoverlapping generations, such that reproduction events along genealogical lines can be repeated at random. We investigate here some of their sample path properties such as asymptotic growth rates and survival, for which the effects of reinforcement on the evolution appear quite strikingly.