偶极<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/D38E86D7-806C-4c48-B7E8-C3F51BD6B569-M001.jpg"><?fx-imagestate width="15.40933418" height="7.45066643"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/D38E86D7-806C-4c48-B7E8-C3F51BD6B569-M001c.jpg"><?fx-imagestate width="15.40933418" height="7.45066643"?></graphic></alternatives></inline-formula>迹与圆盘相交的概率估计

牛冰洁; 蓝师义

doi:10.13471/j.cnki.acta.snus.2022A026

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偶极

S L E_{κ}

迹与圆盘相交的概率估计

研究论文 | 更新时间：2023-12-08

- 偶极 $S L E_{κ}$ 迹与圆盘相交的概率估计
- Estimate of the probability that the dipolar $S L E_{κ}$ trace intersects disks
- 中山大学学报(自然科学版)(中英文) 2023年62卷第6期页码：143-151
- 作者机构：
  
  广西民族大学数学与物理学院，广西南宁 530006
- 作者简介：
  
  牛冰洁（1997年生），女；研究方向：随机Loewner演变；E-mail：1480560354@qq.com
  蓝师义（1966年生），男；研究方向：随机Loewner演变；E-mail：lanshiyi@gxmzu.edu.cn
- 基金信息：
  
  国家自然科学基金(11661011;12161008);广西混杂计算与集成电路设计分析重点实验室项目;广西民族大学研究生创新项目(gxun-chxps202073)
- DOI：10.13471/j.cnki.acta.snus.2022A026
  中图分类号： O211.62
- 纸质出版日期：2023-11-25，
  
  网络出版日期：2023-09-26，
  
  收稿日期：2022-03-16，
  
  录用日期：2022-09-05
扫描看全文
牛冰洁,蓝师义.偶极SLEκ迹与圆盘相交的概率估计[J].中山大学学报(自然科学版),2023,62(06):143-151.

NIU Bingjie,LAN Shiyi.Estimate of the probability that the dipolar SLEκ trace intersects disks[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):143-151.
牛冰洁,蓝师义.偶极SLEκ迹与圆盘相交的概率估计[J].中山大学学报(自然科学版),2023,62(06):143-151. DOI： 10.13471/j.cnki.acta.snus.2022A026.

NIU Bingjie,LAN Shiyi.Estimate of the probability that the dipolar SLEκ trace intersects disks[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):143-151. DOI： 10.13471/j.cnki.acta.snus.2022A026.

偶极

S L E_{κ}

迹与圆盘相交的概率估计

PDF下载

摘要

设

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092735&type=

12.61533356

2.28600001

，首先导出上半平面

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092762&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092741&type=

23.11400032

2.87866688

内从

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092786&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092780&type=

1.60866666

2.28600001

到区间

</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092806&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092771&type=

11.34533310

2.96333337

的偶极

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092868&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092857&type=

6.43466663

3.21733332

迹与圆盘相交的概率表达式；然后，得到带形区域

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092825&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092817&type=

29.71800041

3.80999994

内从

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092842&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092828&type=

1.60866666

2.28600001

到上边界

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092853&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092845&type=

24.72266769

3.80999994

的偶极

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092868&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092857&type=

6.43466663

3.21733332

迹与圆盘相交的概率估计. 这将上半平面

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092873&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092862&type=

2.53999996

2.20133328

内通弦

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092890&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092876&type=

6.43466663

3.21733332

迹的相应概率估计推广到偶极

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093105&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093086&type=

6.43466663

3.21733332

的情形.

Abstract

For

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092914&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092913&type=

15.57866764

2.79399991

， an expression of the probability that the trace of dipolar

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092938&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092918&type=

7.45066643

3.80999994

in the upper half-plane

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092945&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092943&type=

27.77066803

3.30200005

from

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092970&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092950&type=

1.86266661

2.62466669

to interval

</mo><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">]</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092977&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092985&type=

13.20800018

3.47133350

intersects a disk is derived. Next， we obtain an estimate of the probability that the trace of dipolar

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093015&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51092979&type=

7.45066643

3.80999994

in the strip domain

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093020&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093005&type=

35.39066696

4.40266657

from

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093032&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093023&type=

1.86266661

2.70933342

to the upper boundary

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093038&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093043&type=

30.39533424

4.40266657

intersects a disk is obtained. This generalizes the estimate of corresponding probability for chordal

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093053&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093048&type=

7.45066643

3.80999994

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093065&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093062&type=

2.87866688

2.53999996

to the case of dipolar

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093080&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093077&type=

7.45066643

3.80999994

关键词

通弦<math id="M27"><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093091&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093090&type=6.434666633.21733332偶极<math id="M28"><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093105&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093086&type=6.434666633.21733332相交概率

Keywords

chordal<math id="M29"><mtext> </mtext><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093097&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093095&type=8.212666513.89466691dipolar <math id="M30"><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>κ</mi></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093116&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51093113&type=7.450666433.80999994intersection probability

references

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BEFFARA V， 2004. Hausdorff dimensions for<math id="M583"><mtext> </mtext><mi mathvariant="normal">S</mi><mi mathvariant="normal">L</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095804&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51095786&type=7.027333743.30200005［J］. Ann Probab， 32（3B）： 2606-2629.

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LAWLER G F， 2009. Multifractal analysis of the reverse flow for the Schramm-Loewner evolution［M］//BANDT C， et al. ed. Fractal Geometry and Stochastics IV， Progress in Probability， vol 61. Basel： Birkhäuser： 73-107.

LAWLER G F， SCHRAMM O， WERNER W， 2001a. The dimension of the planar Brownian frontier is 4/3［J］. Math Res Lett， 8（4）： 401-411.

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偶极SLEκ迹与圆盘相交的概率估计

Estimate of the probability that the dipolar SLEκ trace intersects disks

DOI：10.13471/j.cnki.acta.snus.2022A026

摘要

Abstract

关键词

Keywords

references

偶极 $S L E_{κ}$ 迹与圆盘相交的概率估计

Estimate of the probability that the dipolar $S L E_{κ}$ trace intersects disks