Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime

Xinxin Chen (1)

1 PSPM - Probabilités, statistique, physique mathématique

We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the $n$-th return to the root, i.e., the number of edges visited more than $k_n$ times. For $k_n=n^\theta$ with $\theta\in(0,1)$, we obtain the convergence in probability of the rescaled heavy range, which improves one result of [AD20].

Mots clés: randomly biased random walk; branching random walk; Seneta-Heyde norming

Domaines: Probabilités [math.PR]

Xinxin Chen. Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime. Stochastic Processes and their Applications, 2022, ⟨10.1016/j.spa.2022.04.018⟩. ⟨hal-02945656v3⟩