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Iterative Schwarz-Christoffel Transformations Driven by Random Walks and Fractal Curves
https://doi.org/10.24789/00001193
https://doi.org/10.24789/00001193bf602cfc-2c7a-4c85-b2a9-ce716a3fc307
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
本文を見る(PDFファイル) (1.0 MB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||||
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| 公開日 | 2012-10-01 | |||||||||
| タイトル | ||||||||||
| タイトル | Iterative Schwarz-Christoffel Transformations Driven by Random Walks and Fractal Curves | |||||||||
| 言語 | en | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| 資源タイプ | departmental bulletin paper | |||||||||
| ID登録 | ||||||||||
| ID登録 | 10.24789/00001193 | |||||||||
| ID登録タイプ | JaLC | |||||||||
| 著者 |
SATO, Fumihito
× SATO, Fumihito
× KATORI, Makoto
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| 著者別名 | ||||||||||
| 識別子Scheme | WEKO | |||||||||
| 識別子 | 23564 | |||||||||
| 姓名 | 佐藤, 史仁 | |||||||||
| 著者別名 | ||||||||||
| 識別子Scheme | WEKO | |||||||||
| 識別子 | 23563 | |||||||||
| 姓名 | 香取, 眞理 | |||||||||
| 抄録 | ||||||||||
| 内容記述タイプ | Abstract | |||||||||
| 内容記述 | Stochastic Loewner evolution (SLE) is a differential equation driven by a onedimensional Brownian motion (BM), whose solution gives a stochastic process of conformal transformation on the upper half complex-plane H. As an evolutionary boundary of image of the transformation, a random curve (the SLE curve) is generated, which is starting from the origin and running in H toward the infinity as time is going. The SLE curves provides a variety of statistical ensembles of important fractal curves, if we change the diffusion constant of the driving BM. In the present paper, we consider the Schwarz-Christoffel transformation (SCT), which is a conformal map from H to the region H with a slit starting from the origin. We prepare a binomial system of SCTs, one of which generates a slit in H with an angle απ from the positive direction of the real axis, and the other of which with an angle (1 −α)π. One parameter κ > 0 is introduced to control the value of α and the length of slit. Driven by a one-dimensional random walk, which is a binomial stochastic process, a random iteration of SCTs is performed. By interpolating tips of slits by straight lines, we have a random path in H, which we call an Iterative SCT (ISCT) path. It is well-known that, as the number of steps N of random walk goes infinity, each path of random walk divided by √N converges to a Brownian curve. Then we expect that the ISCT paths divided by √N (the rescaled ISCT paths) converge to the SLE curves in N → ∞. Our numerical study implies that, for sufficiently large N , the rescaled ISCT paths will have the same statistical properties as the SLE curves have, supporting our expectation. | |||||||||
| 内容記述 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | 【査読有】 | |||||||||
| 書誌情報 |
中央大学理工学研究所論文集 巻 16, p. 1-20, 発行日 2011-03-31 |
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| 出版者 | ||||||||||
| 出版者 | 中央大学理工学研究所 | |||||||||
| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1343-0068 | |||||||||
| 権利 | ||||||||||
| 権利情報 | この資料の著作権は、資料の著作者または学校法人中央大学に帰属します。著作権法が定める私的利用・引用を超える使用を希望される場合には、掲載誌発行部局へお問い合わせください。 | |||||||||
| フォーマット | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | application/pdf | |||||||||
| 著者版フラグ | ||||||||||
| 出版タイプ | VoR | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||
