| A Grain of Dust Falling Through a Sierpinski Gasket |
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| 作者姓名： | Samantha LEORATO Enzo ORSINGHER |
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| 作者单位： | Dipartimento di Statistica, Probabilitd e Statistiche Applicate,University of Rome ＂La Sapienza＂, P. le A. Moro, 5-00185 Roma, Italy |
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| 基金项目： | We gratefully acknowledge the support of the NAT0 grant PST.CLG. 980408. The research is also supported by a grant from MIUR, Italy |
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| 摘 要： | In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket G, where at each layer either absorption or delays are considered. In the case of motion with absorption the explicit distribution of the position of the descending particle in the pre-gasket Gn is obtained and the limiting case of the Sierpinski gasket discussed. For the delayed downward motion we derive a representation of the random time needed to arrive at the base of Gn in terms of independent binomial random variables （containing the contribution of delays at different layers with different geometrical structures）.
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| 关 键 词： | 二项式随机值 分形体 Hausdorff维数 随机通道 自相似性 |
| 收稿时间： | 13 December 2004 |
| 修稿时间： | 2004-12-132005-06-27 |
A Grain of Dust Falling Through a Sierpinski Gasket |
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| Samantha LEORATO Enzo ORSINGHER.A Grain of Dust Falling Through a Sierpinski Gasket[J].Acta Mathematica Sinica,2007,23(6):1095-1108. |
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| Authors: | Samantha Leorato Enzo Orsingher |
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| Institution: | (1) Dipartimento di Statistica, Probabilit′a e Statistiche Applicate, University of Rome “La Sapienza”, P. le A. Moro, 5–00185 Roma, Italy |
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| Abstract: | In this paper we analyze the downward random motion of a particle in a vertical, bounded, Sierpinski gasket G, where at each layer either absorption or delays are considered.
In the case of motion with absorption the explicit distribution of the position of the descending particle in the pre–gasket
G
n
is obtained and the limiting case of the Sierpinski gasket discussed.
For the delayed downward motion we derive a representation of the random time needed to arrive at the base of G
n
in terms of independent binomial random variables (containing the contribution of delays at different layers with different
geometrical structures).
We gratefully acknowledge the support of the NATO grant PST.CLG. 980408. The research is also supported by a grant from MIUR,
Italy |
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| Keywords: | Binomial random variables fractals Hausdorff dimension random walks self-similarity |
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