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

Aliaksandr Radyna

DOI Number
10.2298/FUPCT1603299R
First page
299
Last page
306

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.


Keywords

hierarchical diffusion, random walk, homogeneous tree, Parisi matrix

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References


A. T. Ogielski, D. L. Stein: Dynamics on Ultrametric Spaces, Physical Review Letters. 55, Num.15, (1985), pp. 1634–1637.

V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev: Application of p-adic analysis to models of breaking of replica symmetry. Jour. Phys. A: Math. Gen. 32 (1999) pp.8785–8791.

A. Radyna: m-Adic Multivariate Linear Splines and their Applications to Approximation Theory. In: Proceedings of the International Conference on Functional Analysis and its Applications Dedicated to the 110-th Anniversary of Stefan Banach, May 28-31, 2002, Lviv, Ukraine. North-Holland Mathematics Studies 197, Functional Analysis and its Applications. Elsevier, 2004. pp. 257–266.

A. Khrennikov, A. Radyna: Eigenvalues and Invertibility of Parisi Matrices. Ultramentric Group Point of View. Advanced Studies in Contemporary Mathematica, 8, (2004), No. 2, pp. 95–102.


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