Fetching the paper…
Reading the bibliography…
Using the spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble: $$c_{\delta,\beta}^{(n)} \prod_{1\leq k<l\leq n}| e^{\ii\theta_k}-e^{\ii\theta_l}|^\beta\prod_{j=1}^{n}(1-e^{-\ii\theta_j})^{\delta} (1-e^{\ii\theta_j})^{\overline{\delta}} $$ with $\Re \delta > -1/2$.
F. Dyson, Statistical theory of the energy levels of complex systems. I, II, and III. J. Math. Phys. 3 (1962), 140-156, 157-165, and 166-175
1962
Earlier work this paper cites.
L. K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, Chinese edition: Science Press, Peking, 1958; Russian edition: IL, Moscow, 1959; English edition: Transl. Math. Monographs 6, Amer. Math. Soc., 1963
1963
Earlier work this paper cites.
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York (1972), 9th edition, 258-259
1972
Earlier work this paper cites.
A. Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Higher transcendental functions, Krieger, New-York (1981), I, 15-20
1981
Earlier work this paper cites.
D. Pickrell, Measures on infinite-dimensional Grassmann manifolds, J. Func. Anal. 70 (1987), no. 2, 323-356
1987
Earlier work this paper cites.
G. Ammar, W. Gragg, and L. Reichel, Constructing a unitary Hessenberg matrix from spectral data, Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms (Leuven, 1988), pp. 385-395, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 70
1988
Earlier work this paper cites.
M. L. Mehta, Random matrices. Second edition. Academic Press, Inc., Boston, MA, 1991
1991
Earlier work this paper cites.
D. Pickrell, Mackey analysis of infinite classical motion groups, Pacific J. Math. 150 (1991), 139-166
1991
Earlier work this paper cites.
S. Port, Theoretical Probability for Applications, Wiley, 1994
1994
Earlier work this paper cites.
G. Ben Arous, and A. Guionnet, Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy, Probab. Theory Related Fields, (108) (1997), 517-542
1997
Earlier work this paper cites.
A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer 1998 2nd edition
1998
Earlier work this paper cites.
G.E. Andrews, R.A. Askey, R. Roy, Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, Cambridge, 1999
1999
Earlier work this paper cites.
F. Hiai and D. Petz, A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices, Ann. Inst. H. Poincaré Probab. Statist., 36, (2000), 71-85
2000
Cited alongside, same era.
F. Hiai and D. Petz, The Semicircle Law, Free Random Variables and Entropy, Mathematical Surveys and Monographs, 77 (2000), Amer. Math. Soc., Providence
2000
Cited alongside, same era.
J.P. Keating and N.C. Snaith, Random Matrix Theory and ζ ( 1 / 2 + i t ) \zeta(1/2+it) , Comm. Math. Phys. 214, p 57-89, 2000
2000
Cited alongside, same era.
J.P. Keating and N.C. Snaith, Random matrix theory and L L -functions at s = 1 / 2 s=1/2 , Comm. Math. Phys
2000
Cited alongside, same era.
N.S. Witte and P.J. Forrester, Gap probabilities in the finite and scaled Cauchy random matrix ensembles, Nonlinearity, Vol. 13, 1965-1986, 2000
2000
R. Killip and I. Nenciu, Matrix models for circular ensembles, International Mathematics Research Notices, vol. 2004, no. 50, pp. 2665-2701, 2004
2004
Later among the works it cites.
F. Mezzadri, N.C. Snaith (editors), Recent Perspectives in Random Matrix Theory and Number Theory, London Mathematical Society Lecture Note Series 322 (CUP), (2005)
2005
Later among the works it cites.
B. Simon, OPUC one one foot, Bulletin of the American Mathematical Society, Vol. 42, Number 4, 431-460, 2005
2005
Later among the works it cites.
B. Simon, Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory, AMS Colloquium Publications, Vol. 54.1, American Mathematical Society, Providence, RI, 2005
2005
Later among the works it cites.
B. Simon, Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, AMS Colloquium Publications, Vol. 54.2, American Mathematical Society, Providence, RI, 2005
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
A. Borodin, G. Olshanski, Infinite Random Matrices and Ergodic Measures, Comm. Math. Phys. 203 (2001), 87-123
2001
Cited alongside, same era.
S.V. Khrushchev, Schur’s algorithm, orthogonal polynomials, and convergence of Wall’s continued fractions in L 2 ( 𝕋 ) L^{2}({\mathbb{T}}) , J. Approx. Theory 108 (2) (2001), p. 161-248
2001
Cited alongside, same era.
I. Dumitriu and A. Edelman, Matrix models for beta ensembles. J. Math. Phys. 43 (2002), 5830-5847
2002
Cited alongside, same era.
S.V. Khrushchev, Classification theorems for general orthogonal polynomials on the unit circle, J. Approx. Theory (116) (2) 2002 268–342
2002
Cited alongside, same era.
Yu. A. Neretin, Hua type integrals over unitary groups and over projective limits of unitary groups, Duke Math. J. 114 (2002), 239-266
2002
Cited alongside, same era.
M. J. Cantero, L. Moral, and L. Velazquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra Appl. 362 (2003), 29-56
2003
Cited alongside, same era.
P.J. Forrester and N.S. Witte, Application of the τ \tau -function theory of Painleve equations to random matrices: Pvi, the JUE, CyUE, cJUE and scaled limits, Nagoya Math. J. 174 (2004), p.29-114
2004
Cited alongside, same era.
2005
Later among the works it cites.
P.J. Forrester and E.M. Rains, Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices, International Mathematics Research Notices
2006
Later among the works it cites.
F. Hiai and D. Petz, Large deviations for functions of two random projection matrices, Acta Sci. Math. (Szeged) 72 (2006) 581-609
2006
Later among the works it cites.
R. Killip and I. Nenciu, CMV : The unitary analogue of Jacobi matrices, Communications on Pure and Applied Mathematics, Volume 60, Issue 8, 1148-1188, 2006
2006
Later among the works it cites.
R. Killip and M. Stoiciu, Eigenvalue statistics for CMV matrices: from Poisson to clock via C β \beta E, preprint, arXiv:math-ph/0608002v1, 2006
2006
Later among the works it cites.
B. Simon, CMV matrices: Five years later, J. Comput. Appl. Math., 208: 120-154, 2007
2007
Later among the works it cites.
P. Bourgade, C.P. Hughes, A. Nikeghbali, M. Yor, The characteristic polynomial of a random unitary matrix: a probabilistic approach, Duke Mathematical Journal vol 145, Number 1, 45-69, 2008
2008
Closest in time.