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 (ᵢ) ₁ ₈ ₂₃. Dirichlet environments are weakly elliptic and the walk can be slowdowned by local traps whose strength are governed by a parameter. In this paper we prove a stable limit theorem when the walk is ballistic but subdiffusive, i. e. when (1, 2). This completes the result of Poudevigne (arXiv: 1909. 03866) who proved a sub-ballistic stable limit theorem when (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.