The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble

References

• E. Basor and Y. Chen, Painlevé V and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles, J. Phys. A: Math. Theor. 42 (2009), 035203 (18pp). doi: 10.1088/1751-8113/42/3/035203
   Web of Science ®Google Scholar
• E. Basor and Y. Chen, Perturbed Laguerre unitary ensembles, Hankel determinants, and information theory, Math. Meth. Appl. Sci. 38 (2015), 4840–4851. doi: 10.1002/mma.3399
   Web of Science ®Google Scholar
• E. Basor, Y. Chen and T. Ehrhardt, Painlevé V and time-dependent Jacobi polynomials, J. Phys. A: Math. Theor. 43 (2010), 015204 (25pp). doi: 10.1088/1751-8113/43/1/015204
   Web of Science ®Google Scholar
• E. Basor, Y. Chen and L. Zhang, PDEs satisfied by extreme eigenvalues distributions of GUE and LUE, Random Matrices: Theory and Applications, 1 (2012), 1150003 (21pp). doi: 10.1142/S2010326311500031
   Google Scholar
• M. Chen and Y. Chen, Singular linear statistics of the Laguerre unitary ensemble and Painlevé III. Double scaling analysis, J. Math. Phys. 56 (2015), 063506 (14pp).
   Web of Science ®Google Scholar
• M. Chen, Y. Chen and E. Fan, Perturbed Hankel determinant, correlation functions and Painlevé equations, J. Math. Phys. 57 (2016), 023501 (31pp).
   Web of Science ®Google Scholar
• Y. Chen and D. Dai, Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials, J. Approx. Theory 162 (2010), 2149–2167. doi: 10.1016/j.jat.2010.07.005
   Web of Science ®Google Scholar
• Y. Chen and M.V. Feigin, Painlevé IV and degenerate Gaussian unitary ensembles, J. Phys. A: Math. Gen. 39 (2006), 12381–12393. doi: 10.1088/0305-4470/39/40/007
   Google Scholar
• Y. Chen, N.S. Haq and M.R. McKay, Random matrix models, double-time Painlevé equations, and wireless relaying, J. Math. Phys. 54 (2013), 063506 (55pp).
   Web of Science ®Google Scholar
• Y. Chen, and M.E.H. Ismail, Thermodynamic relations of the Hermitian matrix ensembles, J. Phys. A: Math. Gen. 30 (1997), 6633–6654. doi: 10.1088/0305-4470/30/19/006
   Google Scholar
• Y. Chen and M.E.H. Ismail, Ladder operators and differential equations for orthogonal polynomials, J. Phys. A: Math. Gen. 30 (1997), 7817–7829. doi: 10.1088/0305-4470/30/22/020
   Google Scholar
• Y. Chen and M. Ismail, Jacobi polynomials from compatibility conditions, Proc. Amer. Math. Soc. 133 (2005), 465–472. doi: 10.1090/S0002-9939-04-07566-5
   Web of Science ®Google Scholar
• Y. Chen and A. Its, Painlevé III and a singular linear statistics in Hermitian random matrix ensembles, I, J. Approx. Theory 162 (2010), 270–297. doi: 10.1016/j.jat.2009.05.005
   Web of Science ®Google Scholar
• Y. Chen and N. Lawrence, On the linear statistics of Hermitian random matrices, J. Phys. A: Math. Gen. 31 (1998), 1141–1152. doi: 10.1088/0305-4470/31/4/005
   Google Scholar
• Y. Chen and M.R. McKay, Coulumb fluid, Painlevé transcendents, and the information theory of MIMO systems, IEEE Trans. Inf. Theory 58 (2012), 4594–4634. doi: 10.1109/TIT.2012.2195154
   Web of Science ®Google Scholar
• Y. Chen and G. Pruessner, Orthogonal polynomials with discontinuous weights, J. Phys. A: Math. Gen. 38 (2005), L191–L198. doi: 10.1088/0305-4470/38/12/L01
   Google Scholar
• Y. Chen and L. Zhang, Painlevé VI and the unitary Jacobi ensembles, Stud. Appl. Math. 125 (2010), 91–112.
   Web of Science ®Google Scholar
• D. Dai and L. Zhang, Painlevé VI and Hankel determinants for the generized Jacobi weight, J. Phys. A: Math. Theor. 43 (2010), 055207 (14pp).
   Web of Science ®Google Scholar
• F.J. Dyson, Statistical theory of the energy levels of complex systems. I, II and III, J. Math. Phys. 3 (1962), 140–156, 157–165, 166–175. doi: 10.1063/1.1703773
   Web of Science ®Google Scholar
• I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products 8th ed., (Academic press, 2014).
   Google Scholar
• N.J. Higham, Functions of Matrices: Theory and Computation, (SIAM, 2008).
   Google Scholar
• L.K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, (AMS, 1963).
   Google Scholar
• M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Encyclopedia of Mathematics and its Applications 98, (Cambridge University Press, 2005).
   Google Scholar
• M. Jimbo and T. Miwa, Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II, Physica 2D (1981), 407–448.
   Google Scholar
• N.N. Lebedev, Special Functions & Their Applications, (Dover Publications, INC., New York, 1972).
   Google Scholar
• M. Ledoux and I. Popescu, Mass transportation proofs of free functional inequalities, and free Poincaré inequalities, J. Funct. Anal. 257 (2009), 1175–1221. doi: 10.1016/j.jfa.2009.03.011
   Web of Science ®Google Scholar
• S. Lyu, Y. Chen and E. Fan, Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles, Nucl. Phys. B 926 (2018), 639–670. doi: 10.1016/j.nuclphysb.2017.11.018
   Web of Science ®Google Scholar
• A.P. Magnus, Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials, J. Comput. Appl. Math. 57 (1995), 215–237. doi: 10.1016/0377-0427(93)E0247-J
   Web of Science ®Google Scholar
• M. L. Mehta, Random Matrices 3rd ed., (Elsevier (Singapore) Pte Ltd., Singapore, 2006).
   Google Scholar
• C. Min and Y. Chen, Gap probability distribution of the Jacobi unitary ensemble: an elementary treatment, from finite n to double scaling, Stud. Appl. Math. 140 (2018), 202–220. doi: 10.1111/sapm.12198
   Web of Science ®Google Scholar
• E.B. Saff and V. Totik, Logarithmic Potentials with External Fields, Grundlehren der mathematischen Wissenschaften 316, (Springer-Verlag Berlin Heidelberg GmbH, 1997).
   Google Scholar
• G. Szegö, Orthogonal Polynomials, (AMS, New York, 1939).
   Google Scholar
• C.A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161 (1994), 289–309. doi: 10.1007/BF02099779
   Web of Science ®Google Scholar
• S. Xu, D. Dai and Y. Zhao, Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble, Commun. Math. Phys. 332 (2014), 1257–1296. doi: 10.1007/s00220-014-2131-9
   Web of Science ®Google Scholar