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Volumn 38, Issue 6, 2010, Pages 2443-2485

Applications of Stein's method for concentration inequalities

Author keywords

Concentration inequality; Curie Weiss model; Erdo double acute s R nyi random graph; Exponential random graph; Gibbs measures; Ising model; Large deviation; Stein's method

Indexed keywords


EID: 77957913417     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOP542     Document Type: Article
Times cited : (63)

References (39)
  • 1
    • 33846169811 scopus 로고    scopus 로고
    • Concentration for independent random variables with heavy tails
    • BARTHE, F., CATTIAUX, P. and ROBERTO, C. (2005). Concentration for independent random variables with heavy tails. AMRX Appl. Math. Res. Express 2 39-60.
    • (2005) AMRX Appl. Math. Res. Express , vol.2 , pp. 39-60
    • Barthe, F.1    Cattiaux, P.2    Roberto, C.3
  • 2
    • 34147152743 scopus 로고    scopus 로고
    • Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
    • BARTHE, F., CATTIAUX, P. and ROBERTO, C. (2006). Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry. Rev. Mat. Iberoamericana 22 993-1067.
    • (2006) Rev. Mat. Iberoamericana , vol.22 , pp. 993-1067
    • Barthe, F.1    Cattiaux, P.2    Roberto, C.3
  • 3
    • 57949105276 scopus 로고    scopus 로고
    • Mixing time of exponential random graphs
    • IEEE Computer Society, Washington, DC
    • BHAMIDI, S., BRESLER, G. and SLY, A. (2008). Mixing time of exponential random graphs. In Proc. of the 49th Annual IEEE Symp. on FOCS 803-812. IEEE Computer Society, Washington, DC.
    • (2008) Proc. of the 49th Annual IEEE Symp. on FOCS , pp. 803-812
    • Bhamidi, S.1    Bresler, G.2    Sly, A.3
  • 4
    • 34548297030 scopus 로고    scopus 로고
    • Large deviations and isoperimetry over convex probability measures with heavy tails
    • (electronic)
    • BOBKOV, S. G. (2007). Large deviations and isoperimetry over convex probability measures with heavy tails. Electron. J. Probab. 12 1072-1100 (electronic).
    • (2007) Electron. J. Probab. , vol.12 , pp. 1072-1100
    • Bobkov, S.G.1
  • 5
    • 0034553975 scopus 로고    scopus 로고
    • From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
    • BOBKOV, S. G. and LEDOUX, M. (2000). From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities. Geom. Funct. Anal. 10 1028-1052.
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 1028-1052
    • Bobkov, S.G.1    Ledoux, M.2
  • 6
    • 11944253901 scopus 로고    scopus 로고
    • 2nd ed. Cambridge Studies in Advanced Mathematics. Cambridge Univ. Press, Cambridge
    • BOLLOBÁS, B. (2001). Random Graphs, 2nd ed. Cambridge Studies in Advanced Mathematics 73. Cambridge Univ. Press, Cambridge.
    • (2001) Random Graphs , vol.73
    • Bollobás, B.1
  • 7
    • 34250105416 scopus 로고
    • Laplace approximations for sums of independent random vectors. II. Degenerate maxima and manifolds of maxima
    • BOLTHAUSEN, E. (1987). Laplace approximations for sums of independent random vectors. II. Degenerate maxima and manifolds of maxima. Probab. Theory Related Fields 76 167-206.
    • (1987) Probab. Theory Related Fields , vol.76 , pp. 167-206
    • Bolthausen, E.1
  • 9
    • 0038373013 scopus 로고    scopus 로고
    • Concentration inequalities using the entropy method
    • BOUCHERON, S., LUGOSI, G. and MASSART, P. (2003). Concentration inequalities using the entropy method. Ann. Probab. 31 1583-1614.
    • (2003) Ann. Probab. , vol.31 , pp. 1583-1614
    • Boucheron, S.1    Lugosi, G.2    Massart, P.3
  • 11
    • 33847617461 scopus 로고    scopus 로고
    • Stein's method for concentration inequalities
    • CHATTERJEE, S. (2007). Stein's method for concentration inequalities. Probab. Theory Related Fields 138 305-321.
    • (2007) Probab. Theory Related Fields , vol.138 , pp. 305-321
    • Chatterjee, S.1
  • 12
    • 33947318684 scopus 로고    scopus 로고
    • Concentration of Haar measures, with an application to random matrices
    • CHATTERJEE, S. (2007). Concentration of Haar measures, with an application to random matrices. J. Funct. Anal. 245 379-389.
    • (2007) J. Funct. Anal. , vol.245 , pp. 379-389
    • Chatterjee, S.1
  • 15
    • 77956101526 scopus 로고    scopus 로고
    • Moderate deviations in a random graph and for the spectrum of Bernoulli random matrices
    • DÖRING, H. and EICHELSBACHER, P. (2009). Moderate deviations in a random graph and for the spectrum of Bernoulli random matrices. Electron. J. Probab. 14 2636-2656.
    • (2009) Electron. J. Probab. , vol.14 , pp. 2636-2656
    • Döring, H.1    Eichelsbacher, P.2
  • 17
    • 0009004363 scopus 로고
    • The statistics of Curie-Weiss models
    • ELLIS, R. S. and NEWMAN, C. M. (1978). The statistics of Curie-Weiss models. J. Stat. Phys. 19 149-161.
    • (1978) J. Stat. Phys. , vol.19 , pp. 149-161
    • Ellis, R.S.1    Newman, C.M.2
  • 18
    • 0008999076 scopus 로고
    • Limit theorems for sums of dependent random variables occurring in statistical mechanics
    • ELLIS, R. S. and NEWMAN, C. M. (1978). Limit theorems for sums of dependent random variables occurring in statistical mechanics. Z. Wahrsch. Verw. Gebiete 44 117-139.
    • (1978) Z. Wahrsch. Verw. Gebiete , vol.44 , pp. 117-139
    • Ellis, R.S.1    Newman, C.M.2
  • 20
    • 26444510189 scopus 로고    scopus 로고
    • Modified logarithmic Sobolev inequalities and transportation inequalities
    • GENTIL, I., GUILLIN, A. and MICLO, L. (2005). Modified logarithmic Sobolev inequalities and transportation inequalities. Probab. Theory Related Fields 133 409-436.
    • (2005) Probab. Theory Related Fields , vol.133 , pp. 409-436
    • Gentil, I.1    Guillin, A.2    Miclo, L.3
  • 21
    • 34547692594 scopus 로고    scopus 로고
    • Characterization of Talagrand's like transportation-cost inequalities on the real line
    • GOZLAN, N. (2007). Characterization of Talagrand's like transportation-cost inequalities on the real line. J. Funct. Anal. 250 400-425.
    • (2007) J. Funct. Anal. , vol.250 , pp. 400-425
    • Gozlan, N.1
  • 22
    • 77955615958 scopus 로고    scopus 로고
    • Poincare inequalities and dimension free concentration of measure
    • To appear
    • GOZLAN, N. (2010). Poincare inequalities and dimension free concentration of measure. Ann. Inst. H. Poincaré Probab. Statist. To appear.
    • (2010) Ann. Inst. H. Poincaré Probab. Statist.
    • Gozlan, N.1
  • 25
    • 6344222181 scopus 로고    scopus 로고
    • Upper tails for subgraph counts in random graphs
    • JANSON, S., OLESZKIEWICZ, K. and RUCIŃSKI, A. (2004). Upper tails for subgraph counts in random graphs. Israel J. Math. 142 61-92.
    • (2004) Israel J. Math. , vol.142 , pp. 61-92
    • Janson, S.1    Oleszkiewicz, K.2    Ruciński, A.3
  • 26
    • 0242299142 scopus 로고    scopus 로고
    • The infamous upper tail: Probabilistic methods in combinatorial optimization
    • JANSON, S. and RUCIŃSKI, A. (2002). The infamous upper tail: Probabilistic methods in combinatorial optimization. Random Structures Algorithms 20 317-342.
    • (2002) Random Structures Algorithms , vol.20 , pp. 317-342
    • Janson, S.1    Ruciński, A.2
  • 27
    • 2542554995 scopus 로고    scopus 로고
    • Divide and conquer martingales and the number of triangles in a random graph
    • KIM, J. H. and VU, V. H. (2004). Divide and conquer martingales and the number of triangles in a random graph. Random Structures Algorithms 24 166-174.
    • (2004) Random Structures Algorithms , vol.24 , pp. 166-174
    • Kim, J.H.1    Vu, V.H.2
  • 30
    • 0009072290 scopus 로고
    • A Laplace approximation for sums of independent random variables
    • MARTIN-LÖF, A. (1982). A Laplace approximation for sums of independent random variables. Z. Wahrsch. Verw. Gebiete 59 101-115.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 101-115
    • Martin-Löf, A.1
  • 31
    • 36149012281 scopus 로고
    • Crystal statistics. I. A two-dimensional model with an order-disorder transition
    • ONSAGER, L. (1944). Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2) 65 117-149.
    • (1944) Phys. Rev. , vol.65 , Issue.2 , pp. 117-149
    • Onsager, L.1
  • 32
    • 41349102726 scopus 로고    scopus 로고
    • Statistical mechanics of networks
    • PARK, J. and NEWMAN, M. E. J. (2004). Statistical mechanics of networks. Phys. Rev. E (3) 70 066117-066122.
    • (2004) Phys. Rev. E , vol.70 , Issue.3 , pp. 066117-066122
    • Park, J.1    Newman, M.E.J.2
  • 33
    • 27244450636 scopus 로고    scopus 로고
    • Solution for the properties of a clustered network
    • PARK, J. and NEWMAN, M. E. J. (2005). Solution for the properties of a clustered network. Phys. Rev. E 72 026136-026137.
    • (2005) Phys. Rev. E , vol.72 , pp. 026136-026137
    • Park, J.1    Newman, M.E.J.2
  • 34
    • 35948953514 scopus 로고    scopus 로고
    • CLT-related large deviation bounds based on Stein's method
    • RAIČ, M. (2007). CLT-related large deviation bounds based on Stein's method. Adv. in Appl. Probab. 39 731-752.
    • (2007) Adv. in Appl. Probab. , vol.39 , pp. 731-752
    • Raič, M.1
  • 36
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
    • Univ. California Press, Berkeley, CA
    • STEIN, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proc. Sixth Berkeley Symp. Math. Statist. Probab. Vol. II: Probability Theory 583-602. Univ. California Press, Berkeley, CA.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Probab: Probability Theory , vol.2 , pp. 583-602
    • Stein, C.1
  • 38
    • 51249165477 scopus 로고
    • Concentration of measure and isoperimetric inequalities in product spaces
    • TALAGRAND, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publ. Math. Inst. Hautes Études Sci. 81 73-205.
    • (1995) Publ. Math. Inst. Hautes Études Sci. , vol.81 , pp. 73-205
    • Talagrand, M.1
  • 39
    • 0035595391 scopus 로고    scopus 로고
    • A large deviation result on the number of small subgraphs of a random graph
    • VU, V. H. (2001). A large deviation result on the number of small subgraphs of a random graph. Combin. Probab. Comput. 10 79-94.
    • (2001) Combin. Probab. Comput. , vol.10 , pp. 79-94
    • Vu, V.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.