Öz
Kaynakça
- M. Adler and P. van Moerbeke, 1992, A matrix integral solution to two-dimensional Wp-gravity. Commun. Math. Phys. 147, 25-56. google scholar
- A.B. Balantekin, 2000, Character expansions, Itzykson-Zuber integrals, and the QCD partition function. Phys. Rev. D (3) 62, no. 8, 085017. google scholar
- P. M. Bleher and A. B. J. Kuijlaars, 2004, Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not., no. 3, 109-129. google scholar
- P. Deift, 2000, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics 3, Amer. Math. Soc., Providence RI. google scholar
- J. Faraut and A. Koranyi. 1994, Analysis on symmetric cones, Oxford Math. monographs. google scholar
- J. Harnad and A. Yu. Orlov, 2007, Fermionic construction of tau functions and random processes. Phys. D 235 no. 1-2, 168-206. google scholar
- M. Hien, 2007, Periods for irregular singular connections on surface, Math. Ann. 337, 631-669. google scholar
- K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, 1991, From Gauss to Painleve. Vieweg Verlag. google scholar
- K. Inamasu and H. Kimura, 2021, Matrix hypergeometric functions, semi-classical orthogonal polynomials and quantum Painleeequations. Integral Transforms Spec. Funct. 32, no. 5-8, 528-544. google scholar
- H. Kimura and T. Koitabashi, 1996, Normalizer of maximal abelian subgroup of GL(n)and general hypergeometric functions. Kumamoto J. Math. 9, 13-43. google scholar
- M. Kontsevich, 1992, Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys. 147, no. 1, 1-23. google scholar
- M.L. Mehta, 1991, Random matrices. Second edition, Academic Press, Boston, MA. google scholar
- R. J. Muirhead, 1970, Systems of partial differential equations for hypergeometric functions of matrix arguments. Ann. Math. Statistics 41, 991-1001. google scholar
- R. J. Muirhead, 1982, Aspects of Multivariate Statistical Theory, John Wiley & Sons. google scholar
- H. Nagoya, 2011, Hypergeometric Solutions to Schrödinger equations for the quantum Painleve equations. J. Math. Phys. 52, no. 8, 083509. google scholar
On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument
Öz
We investigate the several special functions defined by a matrix integral on the Hermitian matrix space of size n. They are the matrix argument analogues of the Gauss hypergeometric, Kummer’s confluent hypergeometric, the Bessel, the Hermite-Weber and Airy functions which play important roles in the multivariate statistical analysis and the random matrix theory. We give the integral representations for them as functions of eigenvalues of the matrix argument by using the result of Harish-Chandra and Itzykson-Zuber, and give the systems of differential equations for them. We show that these system are holonomic and have the holonomic rank 2 𝑛 using the theory of Gröbner basis.
Anahtar Kelimeler
hypergeometric function matrix integral holonomic system Gröbner basis
Kaynakça
- M. Adler and P. van Moerbeke, 1992, A matrix integral solution to two-dimensional Wp-gravity. Commun. Math. Phys. 147, 25-56. google scholar
- A.B. Balantekin, 2000, Character expansions, Itzykson-Zuber integrals, and the QCD partition function. Phys. Rev. D (3) 62, no. 8, 085017. google scholar
- P. M. Bleher and A. B. J. Kuijlaars, 2004, Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not., no. 3, 109-129. google scholar
- P. Deift, 2000, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics 3, Amer. Math. Soc., Providence RI. google scholar
- J. Faraut and A. Koranyi. 1994, Analysis on symmetric cones, Oxford Math. monographs. google scholar
- J. Harnad and A. Yu. Orlov, 2007, Fermionic construction of tau functions and random processes. Phys. D 235 no. 1-2, 168-206. google scholar
- M. Hien, 2007, Periods for irregular singular connections on surface, Math. Ann. 337, 631-669. google scholar
- K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, 1991, From Gauss to Painleve. Vieweg Verlag. google scholar
- K. Inamasu and H. Kimura, 2021, Matrix hypergeometric functions, semi-classical orthogonal polynomials and quantum Painleeequations. Integral Transforms Spec. Funct. 32, no. 5-8, 528-544. google scholar
- H. Kimura and T. Koitabashi, 1996, Normalizer of maximal abelian subgroup of GL(n)and general hypergeometric functions. Kumamoto J. Math. 9, 13-43. google scholar
- M. Kontsevich, 1992, Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys. 147, no. 1, 1-23. google scholar
- M.L. Mehta, 1991, Random matrices. Second edition, Academic Press, Boston, MA. google scholar
- R. J. Muirhead, 1970, Systems of partial differential equations for hypergeometric functions of matrix arguments. Ann. Math. Statistics 41, 991-1001. google scholar
- R. J. Muirhead, 1982, Aspects of Multivariate Statistical Theory, John Wiley & Sons. google scholar
- H. Nagoya, 2011, Hypergeometric Solutions to Schrödinger equations for the quantum Painleve equations. J. Math. Phys. 52, no. 8, 083509. google scholar
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Matematik (Diğer) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 25 Haziran 2024 |
| Gönderilme Tarihi | 8 Nisan 2024 |
| Kabul Tarihi | 7 Haziran 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 2 Sayı: 1 |
