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Volumn 140, Issue 5, 2012, Pages 1803-1813

Concentration for noncommutative polynomials in random matrices

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EID: 84856153859     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2011-11262-0     Document Type: Article
Times cited : (24)

References (35)
  • 1
    • 33947507174 scopus 로고    scopus 로고
    • Logarithmic Sobolev inequalities and concentration of measure for convex functions and polynomial chaoses
    • MR2163396 (2006h:60028)
    • R. Adamczak, Logarithmic Sobolev inequalities and concentration of measure for convex functions and polynomial chaoses, Bull. Pol. Acad. Sci. Math. 53 (2005), no. 2, 221-238. MR2163396 (2006h:60028)
    • (2005) Bull. Pol. Acad. Sci. Math , vol.53 , Issue.2 , pp. 221-238
    • Adamczak, R.1
  • 2
    • 0036459716 scopus 로고    scopus 로고
    • On the concentration of eigenvalues of random symmetric matrices
    • MR1942311 (2003i:15020)
    • N. Alon, M. Krivelevich, and V. H. Vu, On the concentration of eigenvalues of random symmetric matrices, Israel J. Math. 131 (2002), 259-267. MR1942311 (2003i:15020)
    • (2002) Israel J. Math , vol.131 , pp. 259-267
    • Alon, N.1    Krivelevich, M.2    Vu, V.H.3
  • 4
    • 34249783444 scopus 로고    scopus 로고
    • Strong asymptotic freeness for Wigner and Wishart matrices
    • MR2317545 (2008e:46079)
    • M. Capitaine and C. Donati-Martin, Strong asymptotic freeness for Wigner and Wishart matrices, Indiana Univ. Math. J. 56 (2007), no. 2, 767-803. MR2317545 (2008e:46079)
    • (2007) Indiana Univ. Math. J , vol.56 , Issue.2 , pp. 767-803
    • Capitaine, M.1    Donati-Martin, C.2
  • 5
    • 0012070851 scopus 로고    scopus 로고
    • Local operator theory, random matrices and Banach spaces
    • North-Holland, Amsterdam, MR1863696 (2004f:47002a)
    • K. R. Davidson and S. J. Szarek, Local operator theory, random matrices and Banach spaces, Handbook of the Geometry of Banach Spaces, Vol. 1, North-Holland, Amsterdam, 2001, pp. 317-366. MR1863696 (2004f:47002a)
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 317-366
    • Davidson, K.R.1    Szarek, S.J.2
  • 6
    • 0011376467 scopus 로고
    • All convex invariant functions of hermitian matrices
    • MR0090572 (19:832b)
    • C. Davis, All convex invariant functions of hermitian matrices, Arch. Math. 8 (1957), 276-278. MR0090572 (19:832b)
    • (1957) Arch. Math , vol.8 , pp. 276-278
    • Davis, C.1
  • 7
    • 84967710235 scopus 로고
    • Bounds on the tail probability of U-statistics and quadratic forms
    • MR1261237(95j:60032)
    • V. H. de la Pêna and S. J. Montgomery-Smith, Bounds on the tail probability of U-statistics and quadratic forms, Bull. Amer. Math. Soc. (N.S.) 31 (1994), no. 2, 223-227. MR1261237(95j:60032)
    • (1994) Bull. Amer. Math. Soc. (N.S.) , vol.31 , Issue.2 , pp. 223-227
    • de la Pêna, V.H.1    Montgomery-Smith, S.J.2
  • 8
    • 79953750532 scopus 로고    scopus 로고
    • Random matrix theory: Invariant ensembles and universality
    • Courant Institute of Mathematical Sciences, New York, MR2514781
    • P. Deift and D. Gioev, Random matrix theory: Invariant ensembles and universality, Courant Lecture Notes in Mathematics, vol. 18, Courant Institute of Mathematical Sciences, New York, 2009. MR2514781
    • (2009) Courant Lecture Notes In Mathematics , vol.18
    • Deift, P.1    Gioev, D.2
  • 9
    • 38249006458 scopus 로고
    • On certain free product factors via an extended matrix model
    • MR1207936 (95a:46085)
    • K. Dykema, On certain free product factors via an extended matrix model, J. Funct. Anal. 112 (1993), no. 1, 31-60. MR1207936 (95a:46085)
    • (1993) J. Funct. Anal , vol.112 , Issue.1 , pp. 31-60
    • Dykema, K.1
  • 10
    • 65349143153 scopus 로고    scopus 로고
    • Large random matrices: Lectures on macroscopic asymptotics
    • Springer-Verlag, Berlin, MR2498298 (2010d:60018)
    • A. Guionnet, Large random matrices: Lectures on macroscopic asymptotics, Lecture Notes in Mathematics, vol. 1957, Springer-Verlag, Berlin, 2009. MR2498298 (2010d:60018)
    • (2009) Lecture Notes In Mathematics , vol.1957
    • Guionnet, A.1
  • 11
    • 0001226135 scopus 로고    scopus 로고
    • Concentration of the spectral measure for large matrices
    • electronic, MR1781846 (2001k:15035)
    • A. Guionnet and O. Zeitouni, Concentration of the spectral measure for large matrices, Electron. Comm. Probab. 5 (2000), 119-136 (electronic). MR1781846 (2001k:15035)
    • (2000) Electron. Comm. Probab , vol.5 , pp. 119-136
    • Guionnet, A.1    Zeitouni, O.2
  • 12
    • 30444453807 scopus 로고    scopus 로고
    • A new application of random matrices: Ext(C*red(F2)) isnot a group
    • MR2183281 (2009k:46121)
    • U. Haagerup and S. Thorbjørnsen, A new application of random matrices: Ext(C*red(F2)) isnot a group, Ann. of Math. (2) 162 (2005), no. 2, 711-775. MR2183281 (2009k:46121)
    • (2005) Ann. of Math , vol.162 , Issue.2 , pp. 711-775
    • Haagerup, U.1    Thorbjørnsen, S.2
  • 13
    • 0001454616 scopus 로고    scopus 로고
    • Asymptotic freeness almost everywhere for random matrices
    • MR1804226 (2002c:15042)
    • F. Hiai and D. Petz, Asymptotic freeness almost everywhere for random matrices, Acta Sci. Math. (Szeged) 66 (2000), no. 3/4, 809-834. MR1804226 (2002c:15042)
    • (2000) Acta Sci. Math. (Szeged) , vol.66 , Issue.3-4 , pp. 809-834
    • Hiai, F.1    Petz, D.2
  • 14
    • 0005141929 scopus 로고    scopus 로고
    • The semicircle law, free random variables and entropy
    • American Mathematical Society, Providence, RI, MR1746976 (2001j:46099)
    • F. Hiai and D. Petz, The semicircle law, free random variables and entropy, Mathematical Surveys and Monographs, vol. 77, American Mathematical Society, Providence, RI, 2000. MR1746976 (2001j:46099)
    • (2000) Mathematical Surveys and Monographs , vol.77
    • Hiai, F.1    Petz, D.2
  • 15
    • 84990712091 scopus 로고
    • Poisson approximation for large deviations
    • MR1138428 (93a:60041)
    • S. Janson, Poisson approximation for large deviations, Random Structures Algorithms 1 (1990), no. 2, 221-229. MR1138428 (93a:60041)
    • (1990) Random Structures Algorithms , vol.1 , Issue.2 , pp. 221-229
    • Janson, S.1
  • 16
    • 0040735835 scopus 로고    scopus 로고
    • Concentration of multivariate polynomials and its applications
    • MR1774845 (2002b:05123)
    • J. H. Kim and V. H. Vu, Concentration of multivariate polynomials and its applications, Combinatorica 20 (2000), no. 3, 417-434. MR1774845 (2002b:05123)
    • (2000) Combinatorica , vol.20 , Issue.3 , pp. 417-434
    • Kim, J.H.1    Vu, V.H.2
  • 17
    • 0036604770 scopus 로고    scopus 로고
    • Approximating the independence number and the chromatic number in expected polynomial time
    • MR1885488 (2002m:05181)
    • M. Krivelevich and V. H. Vu, Approximating the independence number and the chromatic number in expected polynomial time, J. Comb. Optim. 6 (2002), no. 2, 143-155. MR1885488 (2002m:05181)
    • (2002) J. Comb. Optim , vol.6 , Issue.2 , pp. 143-155
    • Krivelevich, M.1    Vu, V.H.2
  • 18
    • 33947544423 scopus 로고    scopus 로고
    • Estimates of moments and tails of Gaussian chaoses
    • MR2294983 (2008a:60045)
    • R. Latała, Estimates of moments and tails of Gaussian chaoses, Ann. Probab. 34 (2006), no. 6, 2315-2331. MR2294983 (2008a:60045)
    • (2006) Ann. Probab , vol.34 , Issue.6 , pp. 2315-2331
    • Latała, R.1
  • 19
    • 0012942540 scopus 로고    scopus 로고
    • The concentration of measure phenomenon
    • American Mathematical Society, Providence, RI, MR1849347(2003k:28019)
    • M. Ledoux, The concentration of measure phenomenon, Mathematical Surveys and Monographs, vol. 89, American Mathematical Society, Providence, RI, 2001. MR1849347(2003k:28019)
    • (2001) Mathematical Surveys and Monographs , vol.89
    • Ledoux, M.1
  • 21
    • 2942644632 scopus 로고    scopus 로고
    • Concentration of norms and eigenvalues of random matrices
    • MR2057479 (2005c:46109)
    • M. W. Meckes, Concentration of norms and eigenvalues of random matrices, J. Funct. Anal. 211 (2004), no. 2, 508-524. MR2057479 (2005c:46109)
    • (2004) J. Funct. Anal , vol.211 , Issue.2 , pp. 508-524
    • Meckes, M.W.1
  • 22
    • 0003270948 scopus 로고
    • Asymptotic theory of finite-dimensional normed spaces
    • Springer-Verlag, Berlin, MR856576(87m:46038)
    • V. D. Milman and G. Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986. MR856576(87m:46038)
    • (1986) Lecture Notes In Mathematics , vol.1200
    • Milman, V.D.1    Schechtma, G.N.2
  • 23
    • 33750960799 scopus 로고    scopus 로고
    • Second order freeness and fluctuations of random matrices. II. Unitary random matrices
    • MR2294222(2009c:15027)
    • J. A. Mingo, P. Sniady, and R. Speicher, Second order freeness and fluctuations of random matrices. II. Unitary random matrices, Adv. Math. 209 (2007), no. 1, 212-240. MR2294222(2009c:15027)
    • (2007) Adv. Math , vol.209 , Issue.1 , pp. 212-240
    • Mingo, J.A.1    Sniady, P.2    Speicher, R.3
  • 24
    • 33645944056 scopus 로고    scopus 로고
    • Second order freeness and fluctuations of random matrices. I. Gaussian and Wishart matrices and cyclic Fock spaces
    • MR2216446 (2007h:46080)
    • J. A. Mingo and R. Speicher, Second order freeness and fluctuations of random matrices. I. Gaussian and Wishart matrices and cyclic Fock spaces, J. Funct. Anal. 235 (2006), no. 1, 226-270. MR2216446 (2007h:46080)
    • (2006) J. Funct. Anal , vol.235 , Issue.1 , pp. 226-270
    • Mingo, J.A.1    Speicher, R.2
  • 25
    • 38149027598 scopus 로고    scopus 로고
    • The spectral laws of Hermitian block-matrices with large random blocks
    • MR2365648 (2008m:60038)
    • T. Oraby, The spectral laws of Hermitian block-matrices with large random blocks, Electron. Comm. Probab. 12 (2007), 465-476. MR2365648 (2008m:60038)
    • (2007) Electron. Comm. Probab , vol.12 , pp. 465-476
    • Oraby, T.1
  • 26
    • 0003346020 scopus 로고
    • Convex analysis
    • Princeton University Press, Princeton, NJ, MR0274683 (43:445)
    • R. T. Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, NJ, 1970. MR0274683 (43:445)
    • (1970) Princeton Mathematical Series , vol.28
    • Rockafellar, R.T.1
  • 27
    • 12944259008 scopus 로고    scopus 로고
    • Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases
    • MR2117954 (2005k:46173)
    • H. Schultz, Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases, Probab. Theory Related Fields 131 (2005), no. 2, 261-309. MR2117954 (2005k:46173)
    • (2005) Probab. Theory Related Fields , vol.131 , Issue.2 , pp. 261-309
    • Schultz, H.1
  • 28
    • 84968488047 scopus 로고
    • An isoperimetric theorem on the cube and the Kintchine-Kahane inequalities
    • MR964871 (90h:60016)
    • M. Talagrand, An isoperimetric theorem on the cube and the Kintchine-Kahane inequalities, Proc. Amer. Math. Soc. 104 (1988), no. 3, 905-909. MR964871 (90h:60016)
    • (1988) Proc. Amer. Math. Soc , vol.104 , Issue.3 , pp. 905-909
    • Talagrand, M.1
  • 29
    • 51249165477 scopus 로고
    • Concentration of measure and isoperimetric inequalities in product spaces
    • MR1361756 (97h:60016)
    • M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Inst. Hautes études Sci. Publ. Math. 81 (1995), 73-205. MR1361756 (97h:60016)
    • (1995) Inst. Hautes Études Sci. Publ. Math , vol.81 , pp. 73-205
    • Talagrand, M.1
  • 30
    • 0030489977 scopus 로고    scopus 로고
    • New concentration inequalities in product spaces
    • MR1419006 (99b:60030)
    • M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996), no. 3, 505-563. MR1419006 (99b:60030)
    • (1996) Invent. Math , vol.126 , Issue.3 , pp. 505-563
    • Talagrand, M.1
  • 31
    • 77952241032 scopus 로고    scopus 로고
    • The generic chaining
    • Springer-Verlag, Berlin, MR2133757 (2006b:60006)
    • M. Talagrand, The generic chaining, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2005. MR2133757 (2006b:60006)
    • (2005) Springer Monographs In Mathematics
    • Talagrand, M.1
  • 32
    • 79952433487 scopus 로고    scopus 로고
    • Introduction to the non-asymptotic analysis of random matrices
    • Y. Eldar and G. Kutyniok, eds.), Cambridge University Press, to appear
    • R. Vershynin, Introduction to the non-asymptotic analysis of random matrices, Compressed Sensing: Theory and Applications (Y. Eldar and G. Kutyniok, eds.), Cambridge University Press, to appear. Preprint available at http://arxiv.org/abs/1011.3027.
    • Compressed Sensing: Theory and Applications
    • Vershynin, R.1
  • 33
    • 0000215544 scopus 로고
    • Limit laws for random matrices and free products
    • MR1094052 (92d:46163)
    • D. V. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991), no. 1, 201-220. MR1094052 (92d:46163)
    • (1991) Invent. Math , vol.104 , Issue.1 , pp. 201-220
    • Voiculescu, D.V.1
  • 34
    • 0003341427 scopus 로고
    • Free random variables
    • American Mathematical Society, Providence, RI, MR1217253 (94c:46133)
    • D. V. Voiculescu, K. J. Dykema, and A. Nica, Free random variables, CRM Monograph Series, vol. 1, American Mathematical Society, Providence, RI, 1992. MR1217253 (94c:46133)
    • (1992) CRM Monograph Series , vol.1
    • Voiculescu, D.V.1    Dykema, K.J.2    Nica, A.3
  • 35
    • 0034215936 scopus 로고    scopus 로고
    • On the concentration of multivariate polynomials with small expectation
    • MR1761580 (2001g:60060)
    • V. H. Vu, On the concentration of multivariate polynomials with small expectation, Random Structures Algorithms 16 (2000), no. 4, 344-363. MR1761580 (2001g:60060)
    • (2000) Random Structures Algorithms , vol.16 , Issue.4 , pp. 344-363
    • Vu, V.H.1


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