Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model.

We consider Hermitian random band matrices H in d⩾1<inline-graphic></inline-graphic> dimensions. The matrix elements Hxy,<inline-graphic></inline-graphic> indexed by x,y∈Λ⊂Zd,<inline-graphic></inline-graphic> are independent, uniformly distributed random variable if |x-y|<inline-graphic></inline-graphic> is less than the band width W,  and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ|<inline-graphic></inline-graphic> of the matrix. [ABSTRACT FROM AUTHOR]