Fetching the paper…
Reading the bibliography…
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble.
A. E. Ingham: An integral which occurs in statistics
1933
Earlier work this paper cites.
C. L. Siegel: Über die analytische Theorie der quadratischen Formen
1935
Earlier work this paper cites.
I. M. Gelfand and M. L. Zeitlin: Finite-dimensional representations of the group of unimodular matrices
1950
Earlier work this paper cites.
N. G. de Bruijn: On some multiple integrals involving determinants
1955
Earlier work this paper cites.
Harish-Chandra: Differential operators on a semisimple Lie algebra
1957
Earlier work this paper cites.
Y. L. Luke: The Special Functions and their Approximations: Vol. I
1969
Earlier work this paper cites.
C. Itzykson and J. B. Zuber: The planar approximation II
1980
Earlier work this paper cites.
K. I. Gross and D. S. P. Richards: Total positivity, spherical series, and hypergeometric functions of matrix argument
1989
Earlier work this paper cites.
C. W. J. Beenakker: Random-matrix theory of quantum transport
1997
Earlier work this paper cites.
A. M. Mathai: Jacobians of Matrix Transformations and Functions of Matrix Argument
1997
Earlier work this paper cites.
A. Borodin: Biorthogonal ensembles
1999
Earlier work this paper cites.
P. Deift: Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
1999
Earlier work this paper cites.
A. B. Balantekin: Character expansions, Itzykson-Zuber integrals, and the QCD partition function
2000
Earlier work this paper cites.
K. Zyczkowski and H.-J. Sommers: Truncations of random unitary matrices
2000
Earlier work this paper cites.
A. B. Balantekin: Partition functions in statistical mechanics, symmetric functions, and group representations
2001
Earlier work this paper cites.
B. Hassibi and T. L. Marzetta: Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form
2002
Earlier work this paper cites.
E. Gudowska-Nowak, R. A. Janik, J. Jurkiewicz, and M. A. Nowak: Infinite products of large random matrices and matrix-valued diffusion
2003
Earlier work this paper cites.
M. L. Mehta: Random Matrices
2004
Earlier work this paper cites.
A. M. Tulino and S. Verdú: Random Matrix Theory and Wireless Communications, Foundations and Trends in Communications and Information Theory
2004
Cited alongside, same era.
B. Collins: Product of random projections, Jacobi ensembles and universality problems arising from free probability
2005
Cited alongside, same era.
A. Edelman and N. R. Rao: Random matrix theory
2005
Cited alongside, same era.
W. König: Orthogonal polynomial ensembles in probability theory
2005
Cited alongside, same era.
P. Desrosiers and P. J. Forrester: Asymptotic correlations for Gaussian and Wishart matrices with external source
2006
Cited alongside, same era.
J. Harnad and A. Y. Orlov: Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
G. Akemann, M. Kieburg, and L. Wei: Singular value correlation functions for products of Wishart random matrices
2013
Later among the works it cites.
R. Beals and J. Szmigielski: Meijer G-functions: a gentle introduction
2013
Later among the works it cites.
J. R. Ipsen: Products of independent quaternion Ginibre matrices and their correlation functions
2013
Later among the works it cites.
G. Akemann, Z. Burda, M. Kieburg, and T. Nagao: Universal microscopic correlation functions for products of truncated unitary matrices
2014
Later among the works it cites.
M. Bertola and T. Bothner: Universality conjecture and results for a model of several coupled positive-definite matrices
2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2006
Cited alongside, same era.
J. E. Bunder, K. B. Efetov, K. B. Kravtsov, O. M. Yevtushenko, and M. R. Zirnbauer: Superbosonization formula and its application to random matrix theory
2007
Cited alongside, same era.
A. Huckleberry, A. Puettmann, and M. R. Zirnbauer: Haar expectations of ratios of random characteristic polynomials
2007
Cited alongside, same era.
P. Deift and D. Gioev: Random Matrix Theory: Invariant Ensembles and Universality
2009
Cited alongside, same era.
P. H. Damgaard, K. Splittorff, and J. J. M. Verbaarschot: Microscopic spectrum of the Wilson Dirac operator
2010
Cited alongside, same era.
P. J. Forrester: Log-Gases and Random Matrices
2010
Cited alongside, same era.
E. Kanzieper and N. Singh: Non-Hermitean Wishart random matrices (I)
2010
Cited alongside, same era.
M. Bertola, M. Gekhtman, and J. Szmigielski, Cauchy-Laguerre two-matrix model and the Meijer-G random point field, Comm. Math. Phys. 326
2014
Later among the works it cites.
K. Coulembier and M. Kieburg: Pizzetti formulae for Stiefel manifolds and applications
2014
Later among the works it cites.
P. J. Forrester: Probability of all eigenvalues real for products of standard Gaussian matrices
2014
Later among the works it cites.
P. J. Forrester: Eigenvalue statistics for product complex Wishart matrices
2014
Later among the works it cites.
P. J. Forrester and M. Kieburg: Relating the Bures measure to the Cauchy two-matrix model
2014
Later among the works it cites.
P. J. Forrester, D-Z. Liu, and P. Zinn-Justin: Equilibrium problems for Raney densities
2014
Later among the works it cites.
J. R. Ipsen and M. Kieburg: Weak commutation relations and eigenvalue statistics for products of rectangular random matrices
2014
Later among the works it cites.
A. B. J. Kuijlaars and D. Stivigny: Singular values of products of random matrices and polynomial ensembles
2014
Later among the works it cites.
A. B. J. Kuijlaars and L. Zhang: Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
2014
Later among the works it cites.
D.-Z. Liu, D. Wang, and L. Zhang: Bulk and soft-edge universality for singular values of products of Ginibre random matrices
2014
Later among the works it cites.
E. Strahov: Differential equations for singular values of products of Ginibre random matrices
2014
Later among the works it cites.
A. B. J. Kuijlaars: Transformations of polynomial ensembles
2015
Closest in time.