3 papers
math.PR2024
Genealogy in critical generations of a diffusive random walk in random environment on trees
Alexis Kagan
We consider the range , the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk on a Galton-Watson tree up to the…
math.PR2024
The leftmost particle of branching subordinators
Alexis Kagan, Grégoire Véchambre
We define a family of continuous-time branching particle systems on the non-negative real line, called branching subordinators, where particles move as independent subordinators. E…
math.PR2024
Local times in critical generations of a random walk in random environment on trees
Alexis Kagan
We consider a null-recurrent randomly biased walk on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a cr…