"Random matrix"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 38번째 줄: | 38번째 줄: | ||
** eigenvalue distributions of the classical Gaussian random matrices ensembles | ** eigenvalue distributions of the classical Gaussian random matrices ensembles | ||
** distribution of their largest eigenvalue in the limit of large matrices | ** distribution of their largest eigenvalue in the limit of large matrices | ||
| − | ** <math>q''(s)=sq(s)+2q(s)^3</math><br> | + | ** <math>q''(s)=sq(s)+2q(s)^3</math> Painleve II equation<br><math>F_2(s)=\exp\left(-\int_{s}^{\infty}(x-s)q^2(x)dx\right)</math><br><math>F_1(s)=\exp\left(-\frac{1}{2}\int_{s}^{\infty}q(x)dx\right)F_2(s)^{1/2}</math><br><math>F_4(s/\sqrt{2})=\cosh\left(\frac{1}{2}\int_{s}^{\infty}q(x)dx\right)F_2(s)^{1/2}</math><br> |
2012년 8월 26일 (일) 15:10 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=
- non-intersecting paths[[3091026|]]
- Macdonald theory
- 리만가설
encyclopedia
- http://mathworld.wolfram.com/WignersSemicircleLaw.html
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- Large random matrices: lectures on macroscopic asymptotics http://www.mathematik.uni-muenchen.de/~lerdos/SS09/Random/guionnetcours.pdf
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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
articles
- A Note on the Eigenvalue Density of Random MatricesMichael K.-H. Kiessling and Herbert Spohn
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1007/s002200050516
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field