Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664613 | Acta Mathematica Scientia | 2011 | 24 Pages |
Abstract
This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)