Alexis Kagan

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math.PR2024

Genealogy in critical generations of a diffusive random walk in random environment on trees

Alexis Kagan

We consider the range $R^{(n)}$ , the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $X$ on a Galton-Watson tree $T$ 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 $X$ on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a cr…

math.PR2023

Scaling limit for local times and return times of a randomly biased walk on a Galton-Watson tree

Alexis Kagan

We consider a null recurrent random walk $X$ on a super-critical Galton Watson marked tree $T$ in the (sub-)diffusive regime. We are interested in the asymptotic…