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## Search Articles

2016, Graduate studies in mathematics, ISBN 9780821848418, Volume 172, xi, 461

Random matrices (probabilistic aspects; for algebraic aspects see 15B52) | Equations of mathematical physics and other areas of application | Partial differential equations | Approximations and expansions | Probability theory and stochastic processes | Special matrices | Operator theory | Probability theory on algebraic and topological structures | Riemann-Hilbert problems | Exact enumeration problems, generating functions | Convex and discrete geometry | Special classes of linear operators | Combinatorics | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) | Time-dependent statistical mechanics (dynamic and nonequilibrium) | Enumerative combinatorics | Exactly solvable dynamic models | Linear and multilinear algebra; matrix theory | Special processes | Statistical mechanics, structure of matter | Toeplitz operators, Hankel operators, Wiener-Hopf operators | Tilings in $2$ dimensions | Interacting random processes; statistical mechanics type models; percolation theory | Discrete geometry | Random matrices | Combinatorial analysis

Book

2011, Mathematical surveys and monographs, ISBN 9780821852859, Volume 171, xiv, 632

Book

2017, Mathematical surveys and monographs, ISBN 9781470434687, Volume no. 223., xxi, 414 pages

Book

2014, CRM monograph series / Centre de Recherches Mathematiques, ISBN 1470409615, Volume 32, ix, 224

Book

2012, Graduate studies in mathematics, ISBN 9780821874301, Volume 132, x, 282

Book

2013, Volume 593

Conference Proceeding

2016, Volume 91

Conference Proceeding

Probability theory and related fields, ISSN 0178-8051, 4/2019, Volume 173, Issue 3, pp. 1301 - 1347

We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let
$$C_1 Anti-concentration | Singularity | 60C05 | Statistics for Business, Management, Economics, Finance, Insurance | Random graphs | Theoretical, Mathematical and Computational Physics | Adjacency matrices | Invertibility | Probability Theory and Stochastic Processes | Mathematics | Primary: 60B20 | Singular probability | Sparse matrices | Operations Research/Decision Theory | Secondary: 46B09 | Regular graphs | Mathematical and Computational Biology | Smallest singular value | Littlewood–Offord theory | 05C80 | Quantitative Finance | 15B52 | 46B06 | Random matrices | Condition number | Statistics & Probability | Physical Sciences | Science & Technology | Computer science | Lower bounds | Parameter estimation | Graph theory

Journal Article

Journal of theoretical probability, ISSN 0894-9840, 12/2016, Volume 29, Issue 4, pp. 1199 - 1239

... Random matrices · Unitary ensemble · Orthogonal polynomials ·
Large deviation principle · Invariance principle
Mathematics Subject Classiﬁcation (2010) 15B52 · 42C05...

15B52 | Random matrices | Large deviation principle | 60F10 | Orthogonal polynomials | Probability Theory and Stochastic Processes | Unitary ensemble | Invariance principle | Mathematics | Statistics, general | 60F17 | 42C05 | Statistics & Probability | Physical Sciences | Science & Technology | Polynomials

15B52 | Random matrices | Large deviation principle | 60F10 | Orthogonal polynomials | Probability Theory and Stochastic Processes | Unitary ensemble | Invariance principle | Mathematics | Statistics, general | 60F17 | 42C05 | Statistics & Probability | Physical Sciences | Science & Technology | Polynomials

Journal Article

Probability theory and related fields, ISSN 0178-8051, 4/2017, Volume 167, Issue 3, pp. 673 - 776

We consider
$$N\times N$$
N
×
N
Hermitian random matrices H consisting of blocks of size
$$M\ge N^{6/7}$$
M
≥
N
6
/
7...

Supersymmetry | 82B44 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Delocalization | 15B52 | Statistics for Business/Economics/Mathematical Finance/Insurance | Local semicircle law | Random band matrix | Operation Research/Decision Theory | 81Q60 | Green’s function comparison | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Localization | Symmetry | Green's functions | Banded structure | Gaussian distribution | Texts | Strategy | Eigenvectors | Spectra | Estimates

Supersymmetry | 82B44 | Mathematical and Computational Biology | Theoretical, Mathematical and Computational Physics | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Delocalization | 15B52 | Statistics for Business/Economics/Mathematical Finance/Insurance | Local semicircle law | Random band matrix | Operation Research/Decision Theory | 81Q60 | Green’s function comparison | Statistics & Probability | Physical Sciences | Science & Technology | Studies | Localization | Symmetry | Green's functions | Banded structure | Gaussian distribution | Texts | Strategy | Eigenvectors | Spectra | Estimates

Journal Article

Constructive approximation, ISSN 0176-4276, 4/2014, Volume 39, Issue 2, pp. 273 - 322

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral), and Jacobi β-ensembles of N×N random matrices. More specifically...

15B52 | Random matrices | Numerical Analysis | Analysis | Steepest descent method | Jack polynomials | 05E05 | Beta-ensembles | Mathematics | 41A60 | 33C70 | Multivariate hypergeometric functions | Physical Sciences | Science & Technology

15B52 | Random matrices | Numerical Analysis | Analysis | Steepest descent method | Jack polynomials | 05E05 | Beta-ensembles | Mathematics | 41A60 | 33C70 | Multivariate hypergeometric functions | Physical Sciences | Science & Technology

Journal Article

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