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，是中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，从事概率论研究。1985年起任教授，1990年起为博士生导师，其 间1986年10月至1987年9月曾任英国Edinburgh大学研究员。2003年起为中国科学院院士。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；找到了诸不等式的显式判别准则和关系图，拓宽了遍历理论，发展了谱理论；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；彻底解决了"转移概率函数的可微性"等难题，建立了跳过程的系统理论。


研究兴趣主要在以下三个方面：

马尔科夫链和马氏跳过程
交互作用粒子系统和随机场
遍历的收敛速率和谱理论
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 ; Reprinted by World Publishing Corporation, Beijing, 1994, Corrections in . Second Edition World Scientific, Singapore, 2004, Prefaces in , and bibiograph in

[4] Ergodic Convergence Rates of Markov Processes—Eigenvalues, Inequalities and Ergodic Theory,

[5] Eigenvalues, inequalities, and Ergodic Theory, Springer, 2004. Preface and contents in

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，1977，3，117-134

[2] 关于解析集的一点注记，北京师大学报，1979，1，45-46

[3] 一类算子方程的最小正解，北京师大学报，1979，3，66-73

[4] 试论“必须设对照试验的优选法”，北京师大学报，1979，4，1-6

[5] 强马氏性研究，长沙铁道学院学报，1979，与侯振挺合作

1980 - 1989：

[6] 马尔可夫过程与场论，科学通报，1980，25，807-811，与侯振挺合作

[7] 一类Q过程的有势性，北京师大学报，1980，3/4，1-12，与侯振挺合作

[8] 抽象空间中的可逆马尔可夫过程，数学年刊，1980，1，437-451

[9] 紧邻速度函数的拟可逆测度，数学年刊，1981，2，47-59，与丁万鼎合作

[10] ωB方程及其在瞬时Q过程构造论中的应用，北京师大学报，1981，4，1-15，与程汉生合作

[11] 有限流出有势Q过程，数学学报，1982，25，136-166

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

[13] 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

[14] 抽象空间中q过程的唯一性准则, 中国科学,1982,4 (中文版),298-308；1983,1(英文版),11-24，与郑小谷合作

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

[16] 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

[17] 马链的基本耦合，北京师大学报，1984 ，4，3-10

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

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

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

[21] 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

[22] 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，1986，1:1，104-117

[23] Existence theorems for interacting particle systems with non-compact state spaces, Sci. Sinica, 1986,8(中文版),707-714；1987, 30:2(英文版),148-156

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

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

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

[27] 随机场概论，数学进展，1989,18:3, 294-322

1990 - 1994：

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

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

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

[31] 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

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

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

[34] 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

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

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

[37] Uniqueness of reaction diffusion processes, Chin. Sci. Bulletin, 1990, 17 (Chinese Edition), 1290-1293；1991, 36:12 (English Edition), 969-973

[38] 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

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

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

[41] 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

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

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

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

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

[46] Application of coupling method to the first eigenvalue on manifold, Sci. Sin. (A), 1993, 23:11 (Chinese Edition), 1130-1140；1994, 37:1 (English Edition), 1-14, With F. Y. Wang

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

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

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

[50] 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：

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

[52] 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

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

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

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

[56] 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

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

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

[59] General formula for lower bound of the first eigenvalue on Riemannian manifolds, Sci. Sin., 1997, 27:1 (Chinese Edition), 34-42；40:4 (English Edition), 384-394, With F. Y. Wang

[60] Coupling, spectral gap and related topics (I), Chin. Sci. Bulletin, 1997, 42:14 (Chinese Edition), 1472-1477；42:16 (English Edition), 1321-1327

[61] Coupling, spectral gap and related topics (II), Chin. Sci. Bulletin, 1997, 42:15 (Chinese Edition), 1585-1591；42:17 (English Edition), 1409-141

[62] Coupling, spectral gap and related topics (III), Chin. Sci. Bulletin, 1997, 42:16 (Chinese Edition), 1696-1703；42:18 (English Edition), 1497-1505

[63] Reaction-diffusion processes, Chin. Sci. Bulletin, 1997, 42:23 (Chinese Edition), 2466-2474；1998, 43:17 (English Edition), 1409-1421

[64] 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

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

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

[67] Analytic proof of dual variational formula for the first eigenvalue in dimension one, Sci. in China (A), 1999, 29:4 (Chinese Edition), 327-336；42:8 (English Edition), 805-815

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

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

[70] Eigenvalues, inequalities and ergodic theory, Chin. Sci. Bulletin, 1999, 44:23 (Chinese Edition), 2465-2470；2000, 45:9 (English Edition), 769-774

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

2000 - ：

[72] Cheeger"s inequalities for general symmetric forms and existence criteria for spectral gap, Ann. Probab., 2000, 28:1, 235-257；results published in Chinese Sci. Bull., 1998, 43:14 (Chinese Edition), 1475-1477；43:18 (English Edition),1516-1519, With F. Y. Wang

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

[74] Logarithmic Sobolev inequality for symmetric forms, Sci. in China (A), 2000, 30:3 (Chinese Edition), 203-209；43:6 (English Edition), 601-608

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

[76] Eigenvalues, inequalities and ergodic theory, Chin. Sci. Bulletin, 1999, 44:23 (Chinese Edition), 2465-2470；2000, 45:9 (English Edition), 769-774

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

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

[79] Variational formulas and approximation theorems for the first eigenvalue, Sci. China (A), 2001, 31:1 (Chinese Edition), 28-36；44:4 (English Edition), 409-418

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

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

[82] 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

[83] 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

[84] 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

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

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

[87] 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

[88] 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

[89] 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

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

科普作品：

[1] 关于ROLAND L. DOBRUSHIN 生平和研究工作的注记

[2] 迈好科学研究的第一步

[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

[7] 小传

[8] 谈谈概率论与其它学科的若干交叉

[9] 严士健论文选编--序言

研究组成员：

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。

张余辉：副教授，硕士生导师，主要研究方向为：跳过程与粒子系统。

毛永华：副教授，主要研究方向为：马氏半群与谱理论。

王颖喆：讲师，主要研究方向为：跳过程与粒子系统。

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

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