On metric structure of ultrametric spaces

Sergei Nechaev; Oleg Vasilyev

doi:10.1088/0305-4470/37/12/005

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arXiv · cond-mat/0310079

On metric structure of ultrametric spaces

Sergei Nechaev·Oleg Vasilyev

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Abstract

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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BibTeX RIS

Sergei Nechaev, Oleg Vasilyev. 2003-10-03. On metric structure of ultrametric spaces. https://doi.org/10.1088/0305-4470%2F37%2F12%2F005

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