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

Kumiko Hattori

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Abstract

Abstract. We determine the ‘exact Hausdorff dimension ’ for a class of multi-type random constructions. As an application, we con-sider 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. 1.

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Abstract. We determine the ‘exact Hausdorff dimension ’ for a class of multi-type random constructions. As an application, we con-sider 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. 1.

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Available abstract

Abstract. We determine the ‘exact Hausdorff dimension ’ for a class of multi-type random constructions. As an application, we con-sider 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. 1.

Key concepts: Hausdorff dimension, Sierpinski triangle, Packing dimension, Mathematics, Dimension function, Limit (mathematics), Hausdorff measure, Effective dimension

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