陈木法,教授,博士生导师,院士。1983年11月获北京师范大学理学博士学位,是我国自己培养的第一批博士之一。自1980年起任教于北京师范大学数学系(今数学学院),从事概率论研究。1985年起任教授,1990年起为博士生导师,期间1986年10月至1987年9月曾任英国Edinburgh大学海外研究员。分别于2003年和2009年当选为中国科学院和第3世界(也称为发展中国家)科学院院士。2012年当选美国数学会Fellow。主要从事概率论与相关领域的研究工作。将概率方法引入第一特征值估计研究并找到了下界估计的统一的变分公式,使得三个方面的主特征值估计得到全面改观;找到了包括Hardy型不等式在内的诸不等式的显式判别准则和关系图,拓宽了随机稳定性理论,发展了谱理论;得到了一维情形各种随机稳定性速度的统一估计;最早研究马氏耦合并得出一条基本定理,更新了耦合理论并开拓了一系列新应用;最先从非平衡统计物理中引进无穷维反应扩散过程,解决了过程的构造、平衡态的存在性和唯一性等根本课题,此方向今已成为国际上粒子系统研究的重要分支;完成了一般或可逆跳过程的唯一性准则并找到唯一性的强有力的充分条件,得到非常广泛的应用;彻底解决"转移概率函数的可微性"等难题,建立了马氏跳过程的系统理论。

研究兴趣主要在以下三个方面:

  1. 马尔可夫链和马氏跳过程
  2. 交互作用粒子系统和随机场
  3. 随机系统的稳定性速度和谱理论

主要专著:

中文专著:

[1] 可逆马氏过程, 湖南科学出版社, 1979,与钱敏、侯振挺等合作

[2] 跳过程与粒子系统,北京师范大学出版社,1986

英文专著:

[3] From Markov Chains to Non-Equilibrium Particle Systems, World Scientific, Singapore, 1992, Corrections in 文件Book3_Corr1.zip;  Reprinted by World Publishing Corporation, Beijing, 1994, Corrections in 文件Book3_Corr2.zip. Second Edition World Scientific, Singapore, 2004, Prefaces in , bibiograph in , and corrections in ,

[4] Ergodic Convergence Rates of Markov Processes—Eigenvalues, Inequalities and Ergodic Theory, (自1993年起,大部分研究论文已收入下列汇编) Vol. 1, Vol. 2, Vol.3, Vol.4

[5] Eigenvalues, inequalities, and Ergodic Theory, Springer, 2005. Preface and contents, and corrections

教材:

[6] 随机过程导论,高等教育出版社,2007,与毛永华合作

文章:

1977 - 1979

[1]    论不定次(批)数条件下单因数优选问题的最优策略,贵阳师院学报,1977,3117-134

[2]  关于解析集的一点注记,北京师大学报,1979145-46

[3]  一类算子方程的最小正解,北京师大学报,1979366-73

[4]  试论“必须设对照试验的优选法”,北京师大学报,197941-6

[5]  强马氏性研究,长沙铁道学院学报,1979,与侯振挺合作

[6] 有势$Q$过程的若干例子, 铁道科学与工程学报(原长沙铁道学院学报), 1979年 4期, 9-20, 与侯振挺合作

1980 - 1989

[7]  马尔可夫过程与场论,科学通报,198025,807-811,与侯振挺合作

[8]  一类Q过程的有势性,北京师大学报,19803/4,1-12,与侯振挺合作

[9]  抽象空间中的可逆马尔可夫过程,数学年刊19801437-451

[10]  紧邻速度函数的拟可逆测度,数学年刊,1981247-59丁万鼎合作

[11]  ωB方程及其在瞬时Q过程构造论中的应用,北京师大学报,198141-15程汉生合作

[12]  有限流出有势Q过程,数学学报,198225136-166

[13]   Potentiality and reversibility for general speed functions (I), Chin. Ann. Math., 1982, 3, 571-568, With S. J. Yan and W. D. Ding

[14]  Potentiality and reversibility for general speed functions (II), Compact state spaces, Chin. Ann. Math., 1982, 3, 705-720, With S. J. Yan and W. D. Ding

[15]  抽象空间中q过程的唯一性准则, 中国科学,1982,4 (中文版),298-3081983,1(英文版),11-24,与郑小谷合作

[16]  λπ-invariant measures, Lecture Notes in Math., Seminaire de Probabilites,  XVII, 1983,  986, 205-220, With D.W.Stroock

[17]  环流分解的稳定性和自组织现象,数学物理学报,1983,4:3(中文版),407-418;1984,4:1(英文版),13-26,与严士健合作

[18]  马链的基本耦合,北京师大学报,198443-10

[19]  Infinite dimensional reaction-diffusion processes, Acta Math. Sinica, New Series, 1985, 1:3, 261-273

[20]  Multidimensional Q-processes, Chin. Ann. Math., 1986, 7B:1, 90-110, With S. J. Yan

[21]  Couplings of jump processes, Acta Math. Sinica, New Series, 1986, 2:2, 123-136

[22]  概率核的存在性和转移函数的可微性,北京师大学报,1986,4, 6-9

[23]  概率论的一些进展,中国数学会50周年大会综合报告,数学季刊,19861:1104-117

[24]  Existence theorems for interacting particle systems with non-compact state spaces, Sci. Sinica, 1986,8(中文版),707-7141987, 30:2(英文版),148-156  

[25]  Stationary distributions of infinite particle systems with non-compact state spaces, Acta Math. Sci., 1989, 9:1, 7-19

[26]  Coupling methods for multidimensional diffusion processes, Ann. Probab., 1989, 17:1, 151-177, With S. F. Li

[27]  Probability metrics and coupling methods, Pitman Research Notes in Math., 1989, 200, 55-72

[28]  随机场概论,数学进展,1989,18:3, 294-322

1990 - 1994:

[29]  Large deviations for Markov chains, Acta Math. Sci. Sin. ,1990, 10:2, 217-222, With Y. G. Lu

[30]  Ergodic theorems for reaction-diffusion processes,  J. Statis. Phys., 1990, 58:5/6, 939-966

[31]  Holder型不等式(上), 数学通报,1990,3, 41-44(下)4, 37-39

[32]  On evaluating the rate function of large deviations for jump processes, Acta Math. Sinica, New Series, 1990, 6:3, 206-219, With  Y. G. Lu

[33]  Dirichlet forms and symmetrizable jump processes, Quart. J. Math., 1991, 6:1, 83-103

[34]  On coupling of jump processes, Chin. Ann. Math., 1991, 12(B): 4, 385-399

[35]  Applications of Malliavin calculus to stochastic differential equations with time-dependent coefficients, Acta Appl. Math. Sin., 1991, 7:3, 193-216, With  X. Y. Zhou

[36]  Exponential L2-convergence and L2-spectral gap for Markov processes, Acta Math. Sinica, New Series, 1991, 7:1, 19-37  

[37]  Comparison theorems for Green functions of Markov chains, Chin. Ann. Math., 1991, 12(B), 206-219

[38]  Uniqueness of reaction diffusion processes, Chin. Sci. Bulletin, 1990, 17 (Chinese Edition),  1290-12931991, 36:12 (English Edition), 969-973

[39]  Jump processes and particle systems, in “Probability Theory and its Applications in China”, edited by S. J. Yan, C. C. Yang and J. G. Wang, Providence, AMS, 1991, 118, 23-57, With  S. J. Yan

[40]  On three classical problems about Markov chains with continuous time parameters, J. Appl. Prob., 1991, 28, 305-320

[41]  Stochastic processes from Yang-Mills lattice field, in “Probability and Statistics, Nankai's Series of Pure and Applied Mathematics”, World Scientific, 1991,

[42]  Hydrodynamic limit for reaction-diffusion processes with several species, in “Probability      and Statistics, Nankai's Series of Pure and Applied Mathematics”, World Scientific, 1991,  With L. P. Huang and X. J. Xu

[43]  Diffusion processes from Yang- Mills lattice field, 1991,  collected in Book[3], With F. Y. Wang

[44]  经济最优化的随机模型(I),应用概率统计, 1992, 8:3, 289- 294

[45]  经济最优化的随机模型(II),应用概率统计,1992 8:4, 374- 377

[46]  On order-preservation and positive correlations for multidimensional diffusion processes, Prob. Th. Rel. Fields, 1993, 95, 421-428, With F. Y. Wang

[47]  Application of coupling method to the first eigenvalue on manifold, Sci. Sin. (A), 1993, 23:11 (Chinese Edition), 1130-11401994, 37:1 (English Edition), 1-14, With  F. Y. Wang

[48]  Ergodicity of reversible reaction-diffusion processes, Acta Math. Sin. New Ser., 1994,10:1, 99-112, With  W. D. Ding and D. G. Zhu

[49]  Stochastic model of economic optimization, J. Beijing Normal Univ., 1994, 30:2, 185-194, With Y. Li

[50]  Optimal Markovian couplings and applications, Acta Math. Sin. New Ser., 1994, 10:3, 260-275

[51]  Optimal couplings and application to Riemannian geometry, Prob. Theory and Math. Stat., 1, Eds. B. Grigelionis et al, 1994, VPS/TEV, 121-142

1995 - 1999

[52]  On the optimality in general sense for odd-block search, Acta Math. Appl. Sin., 1995, 11:4, 389-404, With D. H. Huang

[53]  On ergodic region of Schlogl's model, in Proceedings of International Conference on Dirichlet Forms and Stochastic Processes, Edited by Z. M. Ma, M. Rockner and J. A. Yan, Walter de Gruyter Publishers, 1995, 87-102

[54]  Estimation of the first eigenvalue of second order elliptic operators, J. Funct. Anal., 1995, 131:2, 345-363, With  F. Y. Wang 

[55]  A comment on the book “Continuous-Time Markov Chains” by W. J. Anderson, Chin. J. Appl. Prob. Stat., 1996, 12:1, 55-59

[56]  Estimation of spectral gap for Markov chains, Acta Math. Sin. New Series, 1996, 12:4, 337-360

[57]  The range of random walk on trees and related trapping problem, Acta Math. Appl. Sin., 1997, 13:1, 1-16, With S. J. Yan and X. Y. Zhou

[58]  Estimates of logarithmic Sobolev constant: an improvement of Bakry-Ernery criterion, J. Funct. Anal., 1997, 144:2, 287-300, With F. Y. Wang  

[59]  Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc., 1997, 349:3, 1239-1267, With F. Y. Wang

[60]  General formula for lower bound of the first eigenvalue on Riemannian manifolds, Sci. Sin., 1997, 27:1 (Chinese Edition), 34-4240:4 (English Edition), 384-394, With F. Y. Wang

[61]  Coupling, spectral gap and related topics (I), Chin. Sci. Bulletin, 1997, 42:14 (Chinese Edition), 1472-147742:16 (English Edition), 1321-1327

[62]  Coupling, spectral gap and related topics (II), Chin. Sci. Bulletin, 1997, 42:15 (Chinese Edition), 1585-159142:17 (English Edition), 1409-141

[63]  Coupling, spectral gap and related topics (III), Chin. Sci. Bulletin, 1997, 42:16 (Chinese Edition), 1696-170342:18 (English Edition), 1497-1505

[64]  Reaction-diffusion processes, Chin. Sci. Bulletin, 1997, 42:23 (Chinese Edition), 2466-24741998, 43:17 (English Edition), 1409-1421

[65]  Trilogy of couplings and general formulas for lower bound of spectral gap, in “Probability Towards 2000”, Edited by L. Accardi and C. Heyde, Lecture Notes in Statis., Springer- Verlag, 1998, 128, 123-136

[66]  Estimate of exponential convergence rate in total variation by spectral gap, Acta Math. Sin. Ser. (A), 1998, 41:1, 1-6Acta Math. Sin. New Ser., 1998, 14:1, 9-16

[67]  Single birth processes, Chin. Ann. Math., 1999, 20B:1, 77-82

[68]  Analytic proof of dual variational formula for the first eigenvalue in dimension one, Sci. in China (A), 1999, 29:4 (Chinese Edition), 327-33642:8 (English Edition), 805-815

[69]  Nash inequalities for general symmetric forms, Acta Math. Sin. Eng. Ser., 1999, 15:3, 353-370

[70]  主特征值估计的新故事,数学进展,1999,28:5, 385-392

[71]  Eigenvalues, inequalities and ergodic theory, Chin. Sci. Bulletin, 1999, 44:23 (Chinese Edition), 2465-24702000, 45:9 (English Edition), 769-774

[72]  Eigenvalues, inequalities and ergodic theory (II), Advances in Math., 1999, 28:6, 481-505

2000 - 2009:

[73]  Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap, Ann. Probab., 2000, 28:1, 235-257results published in Chinese Sci. Bull., 1998, 43:14 (Chinese Edition), 1475-147743:18 (English Edition),1516-1519, With F. Y. Wang

[74]  Equivalence of exponential ergodicity and L2-exponential convergence for Markov chains, Stoch. Proc. Appl., 2000, 87, 281-297

[75]  Logarithmic Sobolev inequality for symmetric forms, Sci. in China (A), 2000, 30:3 (Chinese Edition), 203-20943:6 (English Edition), 601-608

[76]  A new story of ergodic theory, to appear in Proceedings of IMS Workshop on Applied Probability, Hong Kong: Intern. Press, 2001

[77]  Eigenvalues, inequalities and ergodic theory, Chin. Sci. Bulletin, 1999, 44:23 (Chinese Edition), 2465-24702000, 45:9 (English Edition), 769-774

[78]  The principal eigenvalue for jump processes, Acta Math. Sin. Eng. Ser., 2000, 16:3, 361-368

[79]  Explicit bounds of the first eigenvalue, Sci. China (A), 2000,39:9 (Chinese Edition), 769-776 43:10 (English Edition), 1051-1059

[80]  Variational formulas and approximation theorems for the first eigenvalue, Sci. China (A), 2001, 31:1 (Chinese Edition), 28-3644:4 (English Edition), 409-418

[81]  Explicit criteria for several types of ergodicity, Chin. J. Appl. Prob. Stat., 2001, 17:2, 1-8

[82]  Algebraic convergence of Markov chains, Ann. Appl. Probab., With Y. Z. Wang, Ann. Appl. Prob. 2003, 13:2, 604-627

[83]  Linear approximation of the first eigenvalue on compact manifolds, With E. Scacciatelli and L. Yao, Sci. China(A), 2001, 31:9 (Chinese Edition), 807-816, 2002, 44:4 (English Edition), 409-418

[84] Ergodic convergence rates of Markov processes -- eigenvalues, inequalities and ergodic theory, in Proceedings of "ICM 2002'', Vol. III, 25-40, 2002, 高等教育出版社

[85] Variational formulas and explicit bounds of Poincare-type inequalities for One-dimensional processes, IMS Lecture Notes--- Monograph Series, Volume 41, 81-96, Probability, Statistics and their Applications: Papers in Honor of Rabi Bhattacharya, 2003

[86] Variational Formulas of Poincare-type Inequalities in Banach Spaces of Functions on the Line, Acta. Math. Sin. Eng. Ser., 2002, 18:3, 417-436

[87] Variational formulas of Poincare-type inequalities for birth-death processes, Acta Math. Sin. Eng. Ser. 2003, 19:4, 625-644

[88] Ten explicit criteria of one-dimensional processes, in "Proceedings of the Conference on Stochastic Analysis on Large Scale Interacting Systems'', Advanced Studies in Pure Mathematics, vol. 39, 89-114, Mathematical Society of Japan, 2004

[89] Dual variational formulas for the first Dirichlet eigenvalue on half-line, With Y. H. Zhang and X. L. Zhao, Sci. China (A) 2003, 33:4 (Chinese Edition), 371-383; (English Edition),46:6, 847-861

[90] Stochastic models of economic optimization, in "RECENT DEVELOPMENTS IN STOCHASTIC ANALYSIS AND RELATED TOPICS--Proceedings of the First Sino-German Conference on Stochastic Analysis (A Satellite Conference of ICM 2002), eds: S. Albeverio, Z.M. Ma and M. Roeckner, World Scientific, 2005

[91] Capacitary criteria for Poincare-type inequalities, Potential Analysis, Vol. 23, No. 4, 2005, 303-322

[92] Exponential convergence rate in entropy, Front. Math. China 2007, 2(3), 329--358

[93] Spectral gap and logarithmic Sobolev constant for continuous spin systems,Acta Math. Sin. New Ser. 24:5(2008), 705--736

2010 -

[94] Speed of stability for birth--death processes,Front. Math. China 5:3 (2010), 379--515

[95] General estimate of the first eigenvalue on manifolds, Front. Math. China 2011, 6(6): 1025--1043

[96] Basic Estimates of Stability Rate for One-dimensional Diffusions, Chapter 6 in ``Probability Approximations and Beyond'', pp. 75--99. Lecture Notes in Statistics 205, Editors: Andrew Barbour, Hock Peng Chan, David Siegmund, 2011/2012

[97] Lower bounds of principal eigenvalue in dimension one, Front. Math. China 7:4, 645--668, 2012

[98] With L.D. Wang and Y.H. Zhang. Mixed principal eigenvalues in dimension one, Front. Math. China 2013, 8(2): 317--343.

[99] Bilateral Hardy-type inequalities, Acta Math. Sin. Eng. Ser. 2013, 29:1, 1--32.

[100] With L.D. Wang and Y.H. Zhang. Mixed eigenvalues of discrete {$p$\,}-Laplacian, Front. Math. China 2014, 9(6): 1261--1292

[101] With L.D. Wang and Y.H. Zhang. Mixed eigenvalues of {$p$\,}-Laplacian, Front. Math. China 2015, 10(2): 249--274

[102] With X. Zhang. Isospectral operators, Communications in Mathematics and Statistics, (2014) 2(1):17--32

[103] With Y.H. Zhang. Unified representation of formulas for single birth processes, Front. Math. China 2014, 9(4): 761--796

[104] Markov Processes and Related Topics, Front. Math. China 2014, 9(4): 715--716

[105] The optimal constant in Hardy-type inequalities, Acta Math. Sin., Eng. Ser. 2015, 31(5): 731--754

[106] Progress on Hardy-type inequalities, Chaper 7 in the book ``Festschrift Masatoshi Fukushima'', 131--142. Eds: Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura, World Scientific 2015

[107} Criteria for Discrete Spectrum of 1D Operators, Commun. Math. 2014, 2(3): 279--309

[108] Criteria for two spectral problems of 1D operators (in Chinese). Sci. Sin. Math. 2015, 45(5), 429--438

[109] Practical Criterion for Uniqueness of $Q$-processes, Chinese Journal of Applied Probability and Statistics, 31(2): 213--224, 2015

[110] Unified speed estimation of various stabilities {\rm (extended abstract)}.
In: Souvenir Booklet of the 24th International Workshop on Matrices and Statistics (25-28 May 2015), Haikou City, Hainan, China. Ed. Jeffrey J. Hunter. Special Matrices 2016; 4: 9--12

[111] Unified Speed Estimation of Various Stabilities, Chinese Journal of Applied Probability and Statistics 2016, 32(1): 1--22

[112] Efficient initials for computing maximal eigenpair, Front. Math. China 2016, 11(6): 1379–1418

A package based on this paper is now available on CRAN through the attached link:

https://cran.r-project.org/web/packages/EfficientMaxEigenpair/index.html

A package in tridiagonal case using MatLab

A package in general case using MatLab

[113] The charming leading eigenpair,Advances in Mathematics (China) 2017, Vol. 46, No. 4, 281–297.

[114] Global algorithms for maximal eigenpair, Front. Math. China 2017, 12(5): 1023–1043.

[115] Trilogy on computing maximal eigenpair, Chapter ?? in “Queueing Theory and Network Applications”, Springer 2017.

科普作品:

[1] 关于ROLAND L. DOBRUSHIN 生平和研究工作的注记 Russian and English translations

[2] 迈好科学研究的第一步 再版:《数学传播》 English translation

[3] 随机系统的数学问题

[4] 相变的数学理论

[5] 第一特征值问题, 《数学通报》, 2002, 8, 0-3

[6] 感谢老师(收入后面的文[18])

[7] 小传小影集

[8] 谈谈概率论与其它学科的若干交叉 再版:《数学传播》

[9] 严士健论文选编--序言

[10] 回忆连家瑶老师的教导

[11] 周先银博士的主要业绩 Preface - In Memory of Dr. Zhou Xianyin

[12]《数学通报》七十周年华诞感言

[13] 谈谈数学素质的培养--院士八闽行福州一中演讲 再版:《数学文化》

[14] 数学的进步 再版:《数学传播》

[15] 双边Hardy不等式及其几何应用数学传播》 数学通报

[16] 网络引领的教育新变革 -《数学文化》 更新版

[17] 如何作学术演讲

[18] 百年院庆感怀

[19] 英文论著里华人名字的写法

[20] 最優搜索問題—從馬航失聯談起

[21] 访谈录

《数学文化》第8卷第3期(2017)

陳木法教授訪談錄-數學傳播41卷4期(2017)

陳木法的自學之旅-數學傳播41卷4期(2017)

 

演讲视频:[点击下载或使用软件下载]

[1] 2002数学家大会 [4.2G]

[2] 学数学与做数学-大学生数学暑期夏令营-2009 [3.2G]

[3] Starting from the first nontrivial eigenvalue-2009 [4.3G]

[4] Starting from stochastic model of economic optimization-2009 [4.3G]

[5] 泉州电视台访谈-2016 [1G]

[6] 网络引领的教育新变革-2016 [13.4G]

[7] 概率论的进步-2016 [12.6G]

[8] 最优搜索问题--从马航失联谈起(四川大学-2016-11-15) [7.6G]

[9] 9-1: Trilogy on computing maximal eigenpair (四川大学-2017-7-6) [2.6G]

9-2: Trilogy on computing maximal eigenpair

(大学生数学暑期夏令营-2017-7-4) [4.9G]

 

研究组成员:

何辉:讲师

洪文明教授,博士生导师,主要研究方向为:Markov过程,测度值分枝过程(超过程)、大偏差、随机环境中的随机游动(RWRE)。

李增沪教授,博士生导师,主要研究方向为:马尔可夫过程(测度值过程、分枝过程、随机微分方程、随机金融模型等)

马宇韬副教授,硕士生导师。

毛永华:教授,主要研究方向为:马氏半群与谱理论。

邵井海:副教授,硕士生导师。

王凤雨教授,博士生导师,主要研究方向为:随机分析、马氏半群与谱理论。

王颖喆: 副教授,主要研究方向为:跳过程与粒子系统。

张梅: 教授,硕士生导师。

张余辉教授,博士生导师,主要研究方向为:跳过程与粒子系统。

何辉:讲师, 主要研究方向为:

相关链接:

学术研究相关网址:

美国数学会 Journal Applied Probability杂志
MCMC Preprint Service - Full List The Probability Web
北京师范大学概率论研究群体 中国数学会概率统计学会

软件下载相关网址:

CCT WinEdt
精品软件秀 家用电脑世界
北京大学软件下载 中国下载

搜索引擎:

Yahoo! 搜狐
Google