The Class of Inverse M-Matrices Associated to Random Walks

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 diagonally dominant, we can take D = E = I. We relate this problem with potentials associated to random walks and study more closely the class of random walks that lose mass at one or two extremes.