THE CLASS OF INVERSE M-MATRICES ASSOCIATED TO RANDOM WALKS∗ CLAUDE DELLACHERIE† , SERVET MARTINEZ‡ , AND JAIME SAN MARTIN‡ Abstract. Given W = M−1, with M a tridiagonal M -matrix, we show that there are two diagonal matrices D,E and two nonsingular ultrametric matrices U, V such that DWE is the Hadamard product of U and V . If M is symmetric and row… (More)

We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a representation theorem for harmonic functions that includes simple expressions for any increasing harmonic function and the Martin… (More)

We prove that the class of GUM matrices is the largest class of bi-potential matrices stable under Hadamard increasing functions. We also show that any power α ≥ 1, in the sense of Hadamard functions, of an inverseM -matrix is also inverseM matrix showing a conjecture stated in Neumann [15]. We study the class of filtered matrices, which include naturally… (More)