| 谈谈概率论与其他学科的若干交叉 |
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| 引用本文： | 陈木法.谈谈概率论与其他学科的若干交叉[J].数学进展,2005,34(6):661-672. |
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| 作者姓名： | 陈木法 |
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| 作者单位： | 北京师范大学数学科学学院,北京,100875 |
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| 基金项目： | 国家自然科学基金委员会创新研究群体项目（No.10121101）、973项目和教育部博士点基金项目. |
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| 摘 要： | 近一二十年以来，概率论获得了很大发展，特别是与其他学科交叉融合，形成了一些新的学科分支和学科生长点．我们首先从2002年国际数学家大会（ICM2002）所反映的情况予以说明．作为这种交融的一个侧面，也概述我们研究群体的三项成果．最后介绍取得这些成果的一种数学工具及其与线性规划和非线性偏微分方程等学科的联系．
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| 关 键 词： | 概率论 ICM2002 随机算法 自由概率 渗流 特征值 遍历理论 最优运输 |
| 文章编号： | 1000-0917（2005）06-661-12 |
| 收稿时间： | 2004-08-03 |
| 修稿时间： | 2004年8月3日 |
Some Interaction of Probability Theory and Other Subjects |
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| CHEN Mu-fa.Some Interaction of Probability Theory and Other Subjects[J].Advances in Mathematics,2005,34(6):661-672. |
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| Authors: | CHEN Mu-fa |
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| Institution: | Department of Mathematics, Beijing Normal University, Beijing, 100875, P, R. China |
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| Abstract: | Remarkable progress in probability theory has been made in the past couple decades. Especially, the interaction of probability theory and other subjects has led to several new branches in mathematics. This point of view was set out by the International Congress of Mathematicians in 2002 (ICM2002). As an additional illustration, three results obtained by our group are surveyed in this paper. Finally, the mathematical tool, used in proving the above results, are introduced and related to other branch of mathematics, such as mathematical programming, partial differential equations, and so on. |
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| Keywords: | Probability theory ICM2002 random algorithm free probability percolation theory eigenvalue ergodic theory optimal transportation |
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