Limit theorem for subdiffusive random walk in Dirichlet random environment in dimension d ≥ 3

We consider random walk in Dirichlet random environment in Zᵈ, d≥ 3, which corresponds to the case where the environment is constructed from i.i.d. transition probabilities at each vertex with a Dirichlet distribution with parameters (αᵢ)1 ≤ i ≤ 2d. Dirichlet environments are weakly elliptic and the walk can be slowdowned by local traps whose strength are governed by a parameter κ. In this paper we prove a stable limit theorem when the walk is ballistic but subdiffusive, i.e. when κ ∈ (1,2). This completes the result of Poudevigne (arXiv:1909.03866) who proved a sub-ballistic stable limit theorem when κ∈ (0,1). Contrary to Poudevigne, we have to assume Sznitman's condition (T) to prove the limit theorem since we work at the level of fluctuations and need a better control on renewal times.