On metric structure of ultrametric spaces

Details On metric structure of ultrametric spaces On metric structure of ultrametric spaces

2003-10-03

arxiv.org/abs/cond-mat/0310079v1

Physics

Condensed Matter

Statistical Mechanics

23 pages, 12 figures

Scientific paper

10.1088/0305-4470/37/12/005

In our work we have reconsidered the old problem of diffusion at the boundary of ultrametric tree from a "number theoretic" point of view. Namely, we use the modular functions (in particular, the Dedekind eta-function) to construct the "continuous" analog of the Cayley tree isometrically embedded in the Poincare upper half-plane. Later we work with this continuous Cayley tree as with a standard function of a complex variable. In the frameworks of our approach the results of Ogielsky and Stein on dynamics on ultrametric spaces are reproduced semi-analytically/semi-numerically. The speculation on the new "geometrical" interpretation of replica n->0 limit is proposed.

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