Exact Hausdorff Dimension of Self-avoiding Processes on the Multi-dimensional Sierpinski Gasket

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J. Math. Sci. Univ. Tokyo
Vol. 7 (2000), No. 1, Page 57--98.

Hattori, Kumiko
Exact Hausdorff Dimension of Self-avoiding Processes on the Multi-dimensional Sierpinski Gasket
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Abstract:
We determine the `exact Hausdorff dimension' for a class of multi-type random constructions. As an application, we consider a model of self-avoiding walk called the `branching model' on the multi-dimensional Sierpinski gasket. We take its continuum limit and determine the exact Hausdorff dimension of the path of the limit process.

Mathematics Subject Classification (1991): Primary 28A70; Secondary 28A80, 60B05, 60G17

Mathematical Reviews Number: MR1749981

Received: 1999-02-23

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