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imported>Pythagoras0 잔글 (찾아 바꾸기 – “* Princeton companion to mathematics(Companion_to_Mathematics.pdf)” 문자열을 “” 문자열로) |
imported>Pythagoras0 |
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| 78번째 줄: | 78번째 줄: | ||
* http://mathworld.wolfram.com/WignersSemicircleLaw.html | * http://mathworld.wolfram.com/WignersSemicircleLaw.html | ||
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| 90번째 줄: | 84번째 줄: | ||
* Large random matrices: lectures on macroscopic asymptotics [http://www.mathematik.uni-muenchen.de/%7Elerdos/SS09/Random/guionnetcours.pdf http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/guionnetcours.pdf] | * Large random matrices: lectures on macroscopic asymptotics [http://www.mathematik.uni-muenchen.de/%7Elerdos/SS09/Random/guionnetcours.pdf http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/guionnetcours.pdf] | ||
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| 105번째 줄: | 94번째 줄: | ||
* http://www.ims.nus.edu.sg/Programs/randommatrix/files/sverdu_p.pdf | * http://www.ims.nus.edu.sg/Programs/randommatrix/files/sverdu_p.pdf | ||
* [http://math.arizona.edu/events/AZschool/material/AZ10-erdos.pdf Universality of Wigner Random Matrices: a Survey of Recent Results] | * [http://math.arizona.edu/events/AZschool/material/AZ10-erdos.pdf Universality of Wigner Random Matrices: a Survey of Recent Results] | ||
| − | * | + | * http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/plan.html |
* Introduction to Random Matrix Theory from An Invitation to Modern Number Theory http://web.williams.edu/go/math/sjmiller/public_html/BrownClasses/54/handouts/IntroRMT_Math54.pdf | * Introduction to Random Matrix Theory from An Invitation to Modern Number Theory http://web.williams.edu/go/math/sjmiller/public_html/BrownClasses/54/handouts/IntroRMT_Math54.pdf | ||
| − | + | * http://stuff.mit.edu/people/raj/Acta05rmt.pdf | |
| 114번째 줄: | 103번째 줄: | ||
==articles== | ==articles== | ||
| − | * [http://dx.doi.org/10.1007/s002200050516%20 A Note on the Eigenvalue Density of Random Matrices]Michael K.-H. Kiessling and Herbert Spohn | + | * [http://dx.doi.org/10.1007/s002200050516%20 A Note on the Eigenvalue Density of Random Matrices]Michael K.-H. Kiessling and Herbert Spohn |
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 11월 6일 (수) 03:45 판
introduction
- The ensembles of random matrices obtained are called Gaussian Orthogonal (GOE), Unitary (GUE), and Symplectic (GSE) Ensembles for = 1, = 2, and = 4 respectively.
- Catalan numbers and random matrices
random self-adjoint matrices
- Wigner matrices
- Band magtrices
- Wishart matrix
- Heavy tails matrices
- Adjacency matrix of Erdos-Renyi graph
Gaussian Wigner matrices
- http://www.math.ucla.edu/~shlyakht/berkeley-07/conference/contrib/peche-talk.pdf
- http://www.math.ucla.edu/~shlyakht/berkeley-07/conference/contrib/guionnet-talk.pdf
Gaussian Unitary Ensemble(GUE) hypothesis
- Wigner's work on neutron scattering resonances
- Hugh Montgomety and Freeman Dyson
- pair correlation function of zeroes of riemann zeta function
- GUE is a big open problem but proven for random matrix models
- GUE Tracy-Widom distribution
- eigenvalue distributions of the classical Gaussian random matrices ensembles
- distribution of their largest eigenvalue in the limit of large matrices
- \(q''(s)=sq(s)+2q(s)^3\) Painleve II equation
\(F_2(s)=\exp\left(-\int_{s}^{\infty}(x-s)q^2(x)dx\right)\)
\(F_1(s)=\exp\left(-\frac{1}{2}\int_{s}^{\infty}q(x)dx\right)F_2(s)^{1/2}\)
\(F_4(s/\sqrt{2})=\cosh\left(\frac{1}{2}\int_{s}^{\infty}q(x)dx\right)F_2(s)^{1/2}\)
determinantal processes
- Random matrices and determinantal processes http://arxiv.org/abs/math-ph/0510038
- http://terrytao.wordpress.com/2009/08/23/determinantal-processes/
history
- 1920-30 studied by statisticians
- 1950 nuclear physics to describe the energy levels distribution of heavy nuclei
- http://www.google.com/search?hl=en&tbs=tl:1&q=
encyclopedia
books
- Large random matrices: lectures on macroscopic asymptotics http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/guionnetcours.pdf
expositions
- Random matrices as a paradigm
- http://www.phys.ust.hk/yilong/research/PhaseSpaceNetHan.pdf
- http://www.ims.nus.edu.sg/Programs/randommatrix/files/sverdu_p.pdf
- Universality of Wigner Random Matrices: a Survey of Recent Results
- http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/plan.html
- Introduction to Random Matrix Theory from An Invitation to Modern Number Theory http://web.williams.edu/go/math/sjmiller/public_html/BrownClasses/54/handouts/IntroRMT_Math54.pdf
- http://stuff.mit.edu/people/raj/Acta05rmt.pdf
articles
- A Note on the Eigenvalue Density of Random MatricesMichael K.-H. Kiessling and Herbert Spohn