HOW TO SOLVE MODEL EQUATION OF HIERARCHICAL DIFFUSION USING SOME MATRIX ALGEBRA

Abstract

Problems of a random walk on a binary tree have been reformulated on any homogeneous tree. Cauchy problem of the random walk for homogeneous and nonhomogeneous equation having a Parisi matrix as a coefficient is formulated and solved with help of a special commutative ring of matrices. The ring containing the Parisi matrix is constructed. The method can be generalized on multidimensional case, for differential equations in non-Archimedean time, and for difference equations.