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D. Bakry and M. Emery, Diffusions hypercontractives, Séminaire de probabilités, XIX, 1983/84, 177–206, Lecture Notes in Math. 1123, Springer, Berlin, 1985. D. Bakry and M. Emery, Diffusions hypercontractives, Séminaire de probabilités, XIX, 1983/84, 177–206, Lecture Notes in Math. 1123, Springer, Berlin, 1985.

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H. Chernoff, A note on an inequality involving the normal distribution, Ann. Probab. 9 (1981), 533–535.  0457.60014 10.1214/aop/1176994428 euclid.aop/1176994428 H. Chernoff, A note on an inequality involving the normal distribution, Ann. Probab. 9 (1981), 533–535.  0457.60014 10.1214/aop/1176994428 euclid.aop/1176994428

3.

F. Chung and S.-T. Yau, Eigenvalues of graphs and Sobolev inequalities, Combin. Probab. Comput. 4 (1995), 11–25.  0843.05073 10.1017/S0963548300001449 F. Chung and S.-T. Yau, Eigenvalues of graphs and Sobolev inequalities, Combin. Probab. Comput. 4 (1995), 11–25.  0843.05073 10.1017/S0963548300001449

4.

F. Chung and S.-T. Yau, A Harnack inequality for homogeneous graphs and subgraphs, Comm. Anal. Geom. 2 (1994), 627–640, also in Turkish J. Math. 19 (1995), 273–290.  0834.05038 10.4310/CAG.1994.v2.n4.a6 F. Chung and S.-T. Yau, A Harnack inequality for homogeneous graphs and subgraphs, Comm. Anal. Geom. 2 (1994), 627–640, also in Turkish J. Math. 19 (1995), 273–290.  0834.05038 10.4310/CAG.1994.v2.n4.a6

5.

F. Chung, A. Grigor'yan and S.-T. Yau, Upper bounds for eigenvalues of the discrete and continuous Laplace operators, Adv. Math. 117 (1996), 165–178. F. Chung, A. Grigor'yan and S.-T. Yau, Upper bounds for eigenvalues of the discrete and continuous Laplace operators, Adv. Math. 117 (1996), 165–178.

6.

F. Chung, R. L. Graham and S.-T. Yau, On sampling with Markov chains, Random Structures and Algorithms 9 (1996), 55–77.  0861.60079 10.1002/(SICI)1098-2418(199608/09)9:1/2<55::AID-RSA4>3.0.CO;2-A F. Chung, R. L. Graham and S.-T. Yau, On sampling with Markov chains, Random Structures and Algorithms 9 (1996), 55–77.  0861.60079 10.1002/(SICI)1098-2418(199608/09)9:1/2<55::AID-RSA4>3.0.CO;2-A

7.

F. Chung, Y. Lin and S.-T. Yau, Harnack inequalities and Logarithmic Harnack inequalities, preprint.  0880.58026 10.4310/MRL.1996.v3.n6.a8 F. Chung, Y. Lin and S.-T. Yau, Harnack inequalities and Logarithmic Harnack inequalities, preprint.  0880.58026 10.4310/MRL.1996.v3.n6.a8

8.

F. Chung and S.-T. Yau, Logarithmic Harnack inequalities, Math. Res. Lett. 3 (1996), 793–812.  0880.58026 10.4310/MRL.1996.v3.n6.a8 F. Chung and S.-T. Yau, Logarithmic Harnack inequalities, Math. Res. Lett. 3 (1996), 793–812.  0880.58026 10.4310/MRL.1996.v3.n6.a8

9.

F. Chung and S.-T. Yau, A combinatorial trace formula, Tsing Hua lectures on geometry & analysis (Hsinchu, 1990–1991), 107–116, Int. Press, Cambridge, MA, 1997. F. Chung and S.-T. Yau, A combinatorial trace formula, Tsing Hua lectures on geometry & analysis (Hsinchu, 1990–1991), 107–116, Int. Press, Cambridge, MA, 1997.

10.

F. Chung, A. Grigor'yan and S.-T. Yau, Eigenvalues and diameters for manifolds and graphs, Tsing Hua lectures on geometry & analysis (Hsinchu, 1990–1991), 79–105, Int. Press, Cambridge, MA, 1997. F. Chung, A. Grigor'yan and S.-T. Yau, Eigenvalues and diameters for manifolds and graphs, Tsing Hua lectures on geometry & analysis (Hsinchu, 1990–1991), 79–105, Int. Press, Cambridge, MA, 1997.

11.

F. Chung and S.-T. Yau, Eigenvalue inequalities for graphs and convex subgraphs, Comm. Anal. Geom. 5 (1997), 575–623.  0902.05047 10.4310/CAG.1997.v5.n4.a1 F. Chung and S.-T. Yau, Eigenvalue inequalities for graphs and convex subgraphs, Comm. Anal. Geom. 5 (1997), 575–623.  0902.05047 10.4310/CAG.1997.v5.n4.a1

12.

F. Chung and S.-T. Yau, Coverings, heat kernels and spanning trees, Electron. J. Combin. 6 (1999), Research Paper 12, 21pp.  0915.05084 F. Chung and S.-T. Yau, Coverings, heat kernels and spanning trees, Electron. J. Combin. 6 (1999), Research Paper 12, 21pp.  0915.05084

13.

F. Chung and S.-T. Yau, Spanning trees in subgraphs of lattices, Contemp. Math. 245, 201–219, Amer. Math. Soc., Providence, R.I., 1999. F. Chung and S.-T. Yau, Spanning trees in subgraphs of lattices, Contemp. Math. 245, 201–219, Amer. Math. Soc., Providence, R.I., 1999.

14.

F. Chung and S.-T. Yau, A Harnack inequality for Dirichlet eigenvalues, J. Graph Theory 34 (2000), 247–257,  0953.05045 10.1002/1097-0118(200008)34:4<247::AID-JGT1>3.0.CO;2-B F. Chung and S.-T. Yau, A Harnack inequality for Dirichlet eigenvalues, J. Graph Theory 34 (2000), 247–257,  0953.05045 10.1002/1097-0118(200008)34:4<247::AID-JGT1>3.0.CO;2-B

15.

F. Chung, A. Grigor'yan and S.-T. Yau, Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs, Comm. Anal. Geom. 8 (2000), 969–1026. F. Chung, A. Grigor'yan and S.-T. Yau, Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs, Comm. Anal. Geom. 8 (2000), 969–1026.

16.

F. Chung and S.-T. Yau, Discrete Green's functions, J. Combin. Theory Ser. A 91 (2000), 191–214.  0963.65120 10.1006/jcta.2000.3094 F. Chung and S.-T. Yau, Discrete Green's functions, J. Combin. Theory Ser. A 91 (2000), 191–214.  0963.65120 10.1006/jcta.2000.3094

17.

Y. Lin and S.-T. Yau, Ricci curvature and eigenvalue estimate on locally finite graphs, Mathematical Research Letters 17 (2010), 345–358.  1232.31003 10.4310/MRL.2010.v17.n2.a13 Y. Lin and S.-T. Yau, Ricci curvature and eigenvalue estimate on locally finite graphs, Mathematical Research Letters 17 (2010), 345–358.  1232.31003 10.4310/MRL.2010.v17.n2.a13

18.

J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2) 169 (2009), 903–991.  1178.53038 10.4007/annals.2009.169.903 J. Lott and C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. (2) 169 (2009), 903–991.  1178.53038 10.4007/annals.2009.169.903

19.

S. Ohta, On measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007), 805–828.  1176.28016 10.4171/CMH/110 S. Ohta, On measure contraction property of metric measure spaces, Comment. Math. Helv. 82 (2007), 805–828.  1176.28016 10.4171/CMH/110

20.

Y. Ollivier, Ricci curvature of Markov chains on metric spaces, J. Funct. Anal. 256 (3) (2009), 810–864.  1181.53015 10.1016/j.jfa.2008.11.001 Y. Ollivier, Ricci curvature of Markov chains on metric spaces, J. Funct. Anal. 256 (3) (2009), 810–864.  1181.53015 10.1016/j.jfa.2008.11.001

21.

K.-T. Sturm, On the geometry of metric measure spaces, (I), (II), Acta Math. 196 (2006), 65–131, 133–177. K.-T. Sturm, On the geometry of metric measure spaces, (I), (II), Acta Math. 196 (2006), 65–131, 133–177.