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2018年随机矩阵理论暑期学校（2018 Summer School on Random Matrix Theory）
2018年 随机矩阵理论 暑期学校
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2017/12/20
We are delighted to organize and host the second edition of the biennial Summer School on Random Matrices at the University of Michigan during June 18--29, 2018.We thank the Michigan Center for Applie...
What is...a Random Matrix?
Random Matrix
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2015/7/8
What is...a Random Matrix。
Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
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2015/1/19
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
A Random Matrix Model for Elliptic Curve $L$-Functions of Finite Conductor
Elliptic Curves Low Lying Zeros n-Level Statistics Random Matrix Theory Jacobi Ensembles Characteristic Polynomial
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2011/9/19
Abstract: We propose a random matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of their critical zeros away from the center of the critical strip was observed b...
Random matrix approach in search for weak signals immersed in background noise
Random matrix approach search signals immersed background noise
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2011/10/17
We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe general ideas a...
Random matrix approach in search for weak signals immersed in background noise
Random matrix weak signals immerse background noise
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2011/8/4
Abstract: We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe gener...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
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2011/7/6
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source, part I
largest eigenvalue of real symmetric Hermitian and Hermitian self-dual random matrix rank one external source
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2011/2/22
We consider the limiting location and limiting distribution of the largest eigenvalue in real
symmetric (β = 1), Hermitian (β = 2), and Hermitian self-dual (β = 4) random matrix models
with rank 1 e...
A generalized plasma and interpolation between classical random matrix ensembles
generalized plasma interpolation classical random matrix ensembles
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2011/1/17
The eigenvalue probability density functions of the classical random matrix ensembles have
a well known analogy with the one component log-gas at the special couplings = 1, 2 and 4.
Random matrix theory of unquenched two-colour QCD with nonzero chemical potential
Spontaneous symmetry breaking matrix models chiral Lagrangians
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2011/3/3
We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero q...
A method for constructing random matrix models of disordered bosons
random matrix models disordered bosons
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2011/2/22
Random matrix models of disordered bosons consist of matrices in the Lie algebra g = spn(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary.
Constraint on periodic orbits of chaotic systems given by Random Matrix Theory
Constraint periodic orbits chaotic systems Random Matrix Theory
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2011/3/4
Considering the fluctuations of spectral functions, we prove that if chaotic systems fulfill the Bohigas-Gianonni-Schmit (BGS) conjecture, which relates their spectral statistics to that of random mat...
How many eigenvalues of a Gaussian random matrix are positive?
Gaussian random matrices large deviations Coulomb gas method index
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2011/3/2
We study the probability distribution of the index N+, i.e., the number of positive eigenvalues of an N × N Gaussian random matrix. We show analytically that, for large N and large N+ with the fractio...
Wilson Fermions, Random Matrix Theory and the Aoki Phase
Wilson Fermions Random Matrix Theory the Aoki Phase
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2011/1/7
The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the moment...
A general and solvable random matrix model for spin decoherence
general solvable random matrix model spin decoherence
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2010/12/1
We propose and solve a simple but very general quantum model of an SU(2)spin interacting with a large external system with N states. The coupling is described by a random hamiltonian in a new general ...