Chen, Mu-Fa: Professor at School of Mathematical Sciences in Beijing Normal University. Academician of Chinese Academy of Sciences and TWAS.

**Main Interests:**

- Markov chains and Markov jump processes
- Interacting particle systems and random fields
- Ergodic convergence rates and spectral theory

[1] Reversible Markov Processes, Hunan Science Press, 1979, With Z. T. Hou, M. Qian, etc.

[2] Jump Processes and Interacting Particle Systems, Beijing Normal Univ. Press, 1986

[3] Introduction to Stochastic Processes (with Y.H. Mao), Higher Edu. Press, 2007

[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 , bibiograph in , and corrections in

[4] Ergodic Convergence Rates of Markov Processes—Eigenvalues, Inequalities and Ergodic Theory, (the most papers since 1993 are collected in following collections) Vol. 1, Vol. 2, Vol.3. Vol.4

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

[6] Introduction to Stochestic Processes，Higher Education Press，2007，with Y. H. Mao (in Chinese)

[1] Optimal method for block-search without knowing the number of experiments, J. Guiyang Teacher's College, 1977, 3, 117-134, (in Chinese)

[2] A remark on analytic sets, J. Beijing Normal Univ., 1979, 1, 45-46, (in Chinese)

[3] The minimal nonnegative solutions for a class of operator equation, J. Beijing Normal Univ., 1979, 3, 66-73, (in Chinese)

[4] On “optimization with comparison tests”, J. Beijing Normal Univ., 1979, 4, 1-6, (in Chinese)

[5] On strong Markov properties, J.Changsha Railway Institute, 1979, With Z. T. Hou, (in Chinese)

[6] Some examples of potential (symmetrizable) $Q$-processes, J. Railway Science and Engineering(i.e. J.Changsha Railway Institute), 1979, 4, 9-20, With Z. T. Hou, (in Chinese)

[7] Markov processes and field theory, Abstract: Kexue Tongbao, 1980, 25, 807-811, collected in Book[1], With Z. T. Hou, (in Chinese)

[8] Potentiality for a class of Q-processes, J. Beijing Normal Univ., 1980, 3/4, 1-12, With Z. T. Hou, (in Chinese)

[9] Reversible Markov processes in abstract spaces, Chin. Ann. Math., 1980, 1, 3-4, 437-451, (in Chinese)

[10] Quasi-reversibility for the nearest speed functions, Chin. Ann. of Math., 1981, 2, 47-59, (in Chinese)

[11] ωB-equation and its application to Q-processes with instantaneous states, J. Beijing Normal Univ., 1981, 4, 1-15, With H. S. Cheng, (in Chinese)

[12] Potential Q-processes with finite exit boundaries, Acta Math. Sinica, 1982, 25, 2, 136-166, (in Chinese)

[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] Uniqueness criteria for q-processes, Sci. Sinica, 1983, 1, 11-24, With X. G. Zheng

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

[17] Stability of circulation decompositions and self-organization phenomena, Acta Math. Scientia, 1984, 4:1, 13-26, With S. J. Yan

[18] Couplings of Markov chains, J. Beijing Normal Univ., 1984, 4, 3-10, (in Chinese)

[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] Existence for a probability kernel and the differentiation properties of transition probability function of jump processes in abstract state spaces, J. Beijing Normal Univ., 1986, 4, 6-9, (in Chinese)

[23] Some new developments in probability theory, Quart. J. Math., 1986, 1:1, 104-117, (in Chinese)

[24] Existence theorems for interacting particle systems with non-compact state spaces, Sci. Sinica, 1986,8 (Chinese Edition), 707-714；1987, 30:2 (English Edition),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] A survey on random fields, Advances in Math., 1989, 18:3, 294-322, (in Chinese)

[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] Inequalities of Holder' type (I), Shuxue Tongbao, 1990, 3, 41-44；(II), 1990, 4, 37-39, (in Chinese)

[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 L^{2}-convergence and L^{2}-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), 1290-1293；1991, 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

[42]
Hydrodynamic limit for reaction-diffusion processes with several species,
in “Probability and Statistics, Nankai's Series
of Pure and Applied Mathematics”, World Scientific,

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

[44] Stochastic models of economic optimization (I), Chin. J. of Appl. Prob. and Statis., 1992, 8:3, 289-294, (in Chinese)

[45] Stochastic models of economic optimization (II), Chin. J. of Appl. Prob. and Statis., 1992, 8:4, 374-377, (in Chinese)

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

[47] 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

[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

[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), 34-42；40:4 (English Edition), 384-394, With F. Y. Wang

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

[62]
Coupling, spectral gap and related topics (II), Chin. Sci. Bulletin, 1997, 42:15
(Chinese Edition), 1585-1591；42:17 (English
Edition), 1409-1416

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

[64] Reaction-diffusion processes, Chin. Sci. Bulletin, 1997, 42:23 (Chinese Edition), 2466-2474；1998, 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, 1-6；Acta
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), 327-336；42:8
(English Edition), 805-815

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

[70] New story on the principal eigenvalues, Advances in Math., 1999, 28:5, 385-392, (in Chinese)

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

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

[73] 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

[74]
Equivalence of exponential ergodicity and L^{2}-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), 203-209；43:6 (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), 2465-2470；2000, 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), 28-36；44:4
(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, Higher Education Press, Beijing, 2002

[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

[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] Mathematical Topics Motivated from Statistical Physics (I) (in Chinese) ---Sci Sin Math

[116] Mathematical Topics Motivated from Statistical Physics (II) (in Chinese) ---Sci Sin Math

**
Popularizing Science Articles：**

[1] Some memories about ROLAND L. DOBRUSHIN (Chinese, Russian and English translations)

[2] Preface - In Memory of Dr. Zhou Xianyin

[3] Making first step toward scientific research. Bernoulli News Vol. 23 (2), 2016, 7--10

[4] A Conversation with Mu-Fa Chen. By Davar Khoshnevisan and Edward Waymire

http://www.ams.org/publications/journals/notices/201706/rnoti-p616.pdf

**Wang,
Fengyu: **Professor. Main interests: Stochastic analysis, Markovian semigroup
and spectrum
theory

**Zhang,
Yuhui: **Associate professor. Main interests: Jump processes and interacting
particle systems

**Mao,
Yonghua: **Associate professor. Main interests: Markovian semigroup and
spectrum theory

**Wang,
Yingzhe:** Associate
professor. Main
interests: Jump processes and interacting
particle systems

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