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References

  • Applegate, David L.; Bixby, Robert E.; Chvátal, Vašek; Cook, William J. The traveling salesman problem. A computational study. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ, 2006. xii+593 pp. ISBN: 978-0-691-12993-8; 0-691-12993-2 MR2286675
  • Remi Bardenet and Odalric-Ambrym Maillard, Concentration inequalities for sampling without replacement, arXiv preprint arXiv:1309.4029 (2013).
  • Boucheron, Stephane; Bousquet, Olivier; Lugosi, Gabor; Massart, Pascal. Moment inequalities for functions of independent random variables. Ann. Probab. 33 (2005), no. 2, 514--560. MR2123200
  • Boucheron, Stephane; Lugosi, Gabor; Massart, Pascal. On concentration of self-bounding functions. Electron. J. Probab. 14 (2009), no. 64, 1884--1899. MR2540852
  • Boucheron, Stephane; Lugosi, Gabor; Massart, Pascal. Concentration inequalities using the entropy method. Ann. Probab. 31 (2003), no. 3, 1583--1614. MR1989444
  • Boucheron, Stephane; Lugosi, Gabor; Massart, Pascal. Concentration inequalities. A nonasymptotic theory of independence. With a foreword by Michel Ledoux. Oxford University Press, Oxford, 2013. x+481 pp. ISBN: 978-0-19-953525-5 MR3185193
  • Chatterjee, Sourav. Concentration inequalities with exchangeable pairs. Thesis (Ph.D.)–Stanford University. ProQuest LLC, Ann Arbor, MI, 2005. 105 pp. ISBN: 978-0542-08643-4 MR2707160
  • Chatterjee, Sourav. Stein's method for concentration inequalities. Probab. Theory Related Fields 138 (2007), no. 1-2, 305--321. MR2288072
  • Chatterjee, Sourav; Diaconis, Persi. Estimating and understanding exponential random graph models. Ann. Statist. 41 (2013), no. 5, 2428--2461. MR3127871
  • Chazottes, J.-R.; Collet, P.; Kulske, C.; Redig, F. Concentration inequalities for random fields via coupling. Probab. Theory Related Fields 137 (2007), no. 1-2, 201--225. MR2278456
  • Djellout, H.; Guillin, A.; Wu, L. Transportation cost-information inequalities and applications to random dynamical systems and diffusions. Ann. Probab. 32 (2004), no. 3B, 2702--2732. MR2078555
  • Dubhashi, Devdatt P.; Panconesi, Alessandro. Concentration of measure for the analysis of randomized algorithms. Cambridge University Press, Cambridge, 2009. xvi+196 pp. ISBN: 978-0-521-88427-3 MR2547432
  • Faden, Arnold M. The existence of regular conditional probabilities: necessary and sufficient conditions. Ann. Probab. 13 (1985), no. 1, 288--298. MR0770643
  • Ghosh, Subhankar; Goldstein, Larry. Concentration of measures via size-biased couplings. Probab. Theory Related Fields 149 (2011), no. 1-2, 271--278. MR2773032
  • Goldstein, Larry; Işlak, Ümit. Concentration inequalities via zero bias couplings. Statist. Probab. Lett. 86 (2014), 17--23. MR3162712
  • Grimmett, Geoffrey R.; Stirzaker, David R. Probability and random processes. Third edition. Oxford University Press, New York, 2001. xii+596 pp. ISBN: 0-19-857223-9 MR2059709
  • Hwang, Frank K.; Richards, Dana S.; Winter, Pawel. The Steiner tree problem. Annals of Discrete Mathematics, 53. North-Holland Publishing Co., Amsterdam, 1992. xii+339 pp. ISBN: 0-444-89098-X MR1192785
  • Komiya, Hidetoshi. Elementary proof for Sion's minimax theorem. Kodai Math. J. 11 (1988), no. 1, 5--7. MR0930413
  • Kulske, Christof. Concentration inequalities for functions of Gibbs fields with application to diffraction and random Gibbs measures. Comm. Math. Phys. 239 (2003), no. 1-2, 29--51. MR1997114
  • Ledoux, Michel. The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9 MR1849347
  • Marton, K. A measure concentration inequality for contracting Markov chains. Geom. Funct. Anal. 6 (1996), no. 3, 556--571. MR1392329
  • Marton, K. Measure concentration and strong mixing. Studia Sci. Math. Hungar. 40 (2003), no. 1-2, 95--113. MR2002993
  • Massart, Pascal. About the constants in Talagrand's concentration inequalities for empirical processes. Ann. Probab. 28 (2000), no. 2, 863--884. MR1782276
  • Ollivier, Yann. A survey of Ricci curvature for metric spaces and Markov chains. Probabilistic approach to geometry, 343--381, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010. MR2648269
  • D. Paulin, Concentration inequalities for Markov chains by Marton couplings and spectral methods, arXiv preprint (2014).
  • Samson, Paul-Marie. Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes. Ann. Probab. 28 (2000), no. 1, 416--461. MR1756011
  • Sion, Maurice. On general minimax theorems. Pacific J. Math. 8 1958 171--176. MR0097026
  • Steele, J. Michael. Probability theory and combinatorial optimization. CBMS-NSF Regional Conference Series in Applied Mathematics, 69. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997. viii+159 pp. ISBN: 0-89871-380-3 MR1422018
  • Talagrand, Michel. Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Etudes Sci. Publ. Math. No. 81 (1995), 73--205. MR1361756
  • Neng-Yi Wang, Concentration inequalities for Gibbs sampling under the d_L^2 metric, Preprint (2014).
  • Neng-Yi Wang and Liming Wu, Convergence rate and concentration inequalities for Gibbs algorithm, To appear in Bernoulli (2014).
  • Wu, Liming. Poincare and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition. Ann. Probab. 34 (2006), no. 5, 1960--1989. MR2271488


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