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.
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