Annals of Probability, ISSN 0091-1798, 2016, Volume 44, Issue 4, pp. 2980 - 3031

The goal of this paper is to establish a relation between characteristic polynomials of N x N GUE random matrices H as N ->infinity, and Gaussian processes...

Mesoscopic regime | Generalized processes | Random matrix theory | Logarithmically correlated | Fractional Brownian motion | UNIVERSALITY | mesoscopic regime | STRONG ASYMPTOTICS | LINEAR EIGENVALUE STATISTICS | STATISTICS & PROBABILITY | fractional Brownian motion | RIEMANN-HILBERT APPROACH | RANDOM MATRICES | generalized processes | MODELS | FLUCTUATIONS | ORTHOGONAL POLYNOMIALS | logarithmically correlated | ALTSHULER-SHKLOVSKII FORMULAS | CENTRAL-LIMIT-THEOREM

Mesoscopic regime | Generalized processes | Random matrix theory | Logarithmically correlated | Fractional Brownian motion | UNIVERSALITY | mesoscopic regime | STRONG ASYMPTOTICS | LINEAR EIGENVALUE STATISTICS | STATISTICS & PROBABILITY | fractional Brownian motion | RIEMANN-HILBERT APPROACH | RANDOM MATRICES | generalized processes | MODELS | FLUCTUATIONS | ORTHOGONAL POLYNOMIALS | logarithmically correlated | ALTSHULER-SHKLOVSKII FORMULAS | CENTRAL-LIMIT-THEOREM

Journal Article

Physical Review B - Condensed Matter and Materials Physics, ISSN 1098-0121, 09/2009, Volume 80, Issue 12

Applying random matrix theory to quantum transport in chaotic cavities, we develop a powerful method for computing the moments of the conductance and...

QUANTUM TRANSPORT | DISTRIBUTIONS | INTEGRALS | PHYSICS, CONDENSED MATTER | RANDOM-MATRIX THEORY | DOTS | POINT CONTACTS | SCATTERING | HYPERGEOMETRIC-FUNCTIONS

QUANTUM TRANSPORT | DISTRIBUTIONS | INTEGRALS | PHYSICS, CONDENSED MATTER | RANDOM-MATRIX THEORY | DOTS | POINT CONTACTS | SCATTERING | HYPERGEOMETRIC-FUNCTIONS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2013, Volume 46, Issue 26, pp. 1 - 10

The K-matrix, also known as the 'Wigner reaction matrix' in nuclear scattering or the 'impedance matrix' in electromagnetic wave scattering, is given...

SYSTEMS | CHARACTERISTIC-POLYNOMIALS | PHYSICS, MULTIDISCIPLINARY | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL | STATISTICS | Matrices (mathematics) | Chaos theory | Mathematical analysis | Electromagnetic waves | Eigenvalues | Blocking | Mathematical models | Density | Invariants

SYSTEMS | CHARACTERISTIC-POLYNOMIALS | PHYSICS, MULTIDISCIPLINARY | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL | STATISTICS | Matrices (mathematics) | Chaos theory | Mathematical analysis | Electromagnetic waves | Eigenvalues | Blocking | Mathematical models | Density | Invariants

Journal Article

Physical Review Letters, ISSN 0031-9007, 1997, Volume 79, Issue 4, pp. 557 - 560

By using the method of orthogonal polynomials, we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from...

GASES | K UI PHYSICS | COMPLEX RANDOM MATRICES | SUPERSYMMETRY | PHYSICS

GASES | K UI PHYSICS | COMPLEX RANDOM MATRICES | SUPERSYMMETRY | PHYSICS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/1996, Volume 37, Issue 10, pp. 5033 - 5060

We study the normalized trace g n (z)=n −1 tr(H−zI)−1 of the resolvent of n×n real symmetric matrices H=[(1+δ jk )W jk √n] j,k=1 n assuming that their entries...

UNIVERSALITY | STATISTICAL PROPERTIES | HAMILTONIANS | PHYSICS, MATHEMATICAL | GRAVITY | ENSEMBLES | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

UNIVERSALITY | STATISTICAL PROPERTIES | HAMILTONIANS | PHYSICS, MATHEMATICAL | GRAVITY | ENSEMBLES | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 01/1991, Volume 62, Issue 1-2, pp. 21 - 33

The thermodynamic equivalence of the large-n limit of the n-vector model in a random external field and the corresponding disordered spherical model is proved....

Random spin systems | ferromagnetic order | FERROMAGNETIC ORDER | SPIN DIMENSIONALITY LIMIT | AXIS MODEL | SYSTEMS | RANDOM SPIN SYSTEMS | SPHERICAL MODEL | PHYSICS, MATHEMATICAL

Random spin systems | ferromagnetic order | FERROMAGNETIC ORDER | SPIN DIMENSIONALITY LIMIT | AXIS MODEL | SYSTEMS | RANDOM SPIN SYSTEMS | SPHERICAL MODEL | PHYSICS, MATHEMATICAL

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 10/1987, Volume 73, Issue 1, pp. 1094 - 1104

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 10/1989, Volume 57, Issue 1-2, pp. 41 - 52

The critical temperature of the generalized spherical model (large-component limit of the classical Heisenberg model) on a cubic lattice, whose every bond is...

critical temperature | decorated lattice | Spherical model | Jacobi matrix | PHYSICS, MATHEMATICAL | GAUSS FUNCTION | THERMODYNAMIC PROPERTIES | NUMERICAL SOLUTION | CLASSICAL MECHANICS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | CRYSTAL STRUCTURE | ONE-DIMENSIONAL CALCULATIONS | CAUCHY PROBLEM | FUNCTIONS | PARTICLE PROPERTIES | CUBIC LATTICES | BOUNDARY CONDITIONS | CRYSTAL MODELS | ANGULAR MOMENTUM | MECHANICS | PHYSICAL PROPERTIES | TRANSITION TEMPERATURE | ORDER PARAMETERS | PHASE TRANSFORMATIONS | FREE ENERGY | 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-) | ENERGY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL MODELS | CRITICAL TEMPERATURE | STATISTICAL MECHANICS | CRYSTAL LATTICES | FINITE DIFFERENCE METHOD | MATRICES | ITERATIVE METHODS | HEISENBERG MODEL | 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

critical temperature | decorated lattice | Spherical model | Jacobi matrix | PHYSICS, MATHEMATICAL | GAUSS FUNCTION | THERMODYNAMIC PROPERTIES | NUMERICAL SOLUTION | CLASSICAL MECHANICS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | CRYSTAL STRUCTURE | ONE-DIMENSIONAL CALCULATIONS | CAUCHY PROBLEM | FUNCTIONS | PARTICLE PROPERTIES | CUBIC LATTICES | BOUNDARY CONDITIONS | CRYSTAL MODELS | ANGULAR MOMENTUM | MECHANICS | PHYSICAL PROPERTIES | TRANSITION TEMPERATURE | ORDER PARAMETERS | PHASE TRANSFORMATIONS | FREE ENERGY | 656002 - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-) | ENERGY | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATHEMATICAL MODELS | CRITICAL TEMPERATURE | STATISTICAL MECHANICS | CRYSTAL LATTICES | FINITE DIFFERENCE METHOD | MATRICES | ITERATIVE METHODS | HEISENBERG MODEL | 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 04/1994, Volume 27, Issue 7, pp. 2527 - 2543

We consider the interband light absorption coefficient (ILAC) for a d-dimensional discrete disordered system, whose Hamiltonian consist of a translation...

PHYSICS

PHYSICS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 06/2009, Volume 42, Issue 22, pp. 222002 - 222002 (8)

We derive an explicit simple formula for expectations of all Schur functions in the real Ginibre ensemble. It is a positive integer for all entries of the...

CHAOS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MATRICES

CHAOS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MATRICES

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2012, Volume 45, Issue 7, pp. 75203 - 31

A generalization of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the...

CIRCULAR LAW | UNITARY | PHYSICS, MULTIDISCIPLINARY | SINGLE RING THEOREM | PHASE-TRANSITION | FORMALISM | PHYSICS, MATHEMATICAL | REAL MATRICES | Functions (mathematics) | Matrices (mathematics) | Mathematical analysis | Eigenvalues | Evolution | Gaussian | Spectral correlation | Matrix methods | Density

CIRCULAR LAW | UNITARY | PHYSICS, MULTIDISCIPLINARY | SINGLE RING THEOREM | PHASE-TRANSITION | FORMALISM | PHYSICS, MATHEMATICAL | REAL MATRICES | Functions (mathematics) | Matrices (mathematics) | Mathematical analysis | Eigenvalues | Evolution | Gaussian | Spectral correlation | Matrix methods | Density

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 10/2010, Volume 82, Issue 4, p. 040106

Statistical properties of nonsymmetric real random matrices of size M, obtained as truncations of random orthogonal NXN matrices, are investigated. We derive...

ENSEMBLE | PHYSICS, FLUIDS & PLASMAS | QUANTUM | RANDOM UNITARY MATRICES | SYSTEMS | PHYSICS, MATHEMATICAL | RESONANCES

ENSEMBLE | PHYSICS, FLUIDS & PLASMAS | QUANTUM | RANDOM UNITARY MATRICES | SYSTEMS | PHYSICS, MATHEMATICAL | RESONANCES

Journal Article

Physics Letters A, ISSN 0375-9601, 1997, Volume 226, Issue 1, pp. 46 - 52

We consider an ensemble of large non-Hermitian random matrices of the form Ĥ + iÂ , where Ĥ and Â are Hermitian statistically independent random N × N...

Complex eigenvalues | Disordered systems | Random matrices | UNIVERSALITY | SUPERSYMMETRY | random matrices | STATISTICS | complex eigenvalues | K UI PHYSICS | PHYSICS | disordered systems

Complex eigenvalues | Disordered systems | Random matrices | UNIVERSALITY | SUPERSYMMETRY | random matrices | STATISTICS | complex eigenvalues | K UI PHYSICS | PHYSICS | disordered systems

Journal Article

Physics Reports, ISSN 0370-1573, 1997, Volume 288, Issue 1, pp. 109 - 126

We discuss the discrete Schrödinger operator H = -Δ + V with surface potential: V as a function of lattice point vanishes outside a surface. In general, the...

Low-dimensional perturbations | Incommensurate structures | Propagation and localization | Surface excitations | propagation and localization | incommensurate structures | LARGE DISORDER | surface excitations | K UI PHYSICS | PHYSICS | low-dimensional perturbations

Low-dimensional perturbations | Incommensurate structures | Propagation and localization | Surface excitations | propagation and localization | incommensurate structures | LARGE DISORDER | surface excitations | K UI PHYSICS | PHYSICS | low-dimensional perturbations

Journal Article

07/1997

Phys. Rev. Lett. Vol.80 (1998) 2897-2900 We develop a theory which describes the behaviour of eigenvalues of a class of one-dimensional random non-Hermitian...

Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Journal Article

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