Download this PDF file Fullscreen Fullscreen Off
References
- Adler, Mark; Cafasso, Mattia; van Moerbeke, Pierre. Fredholm determinants of general $(1,p)$--kernels and reductions ofnon--linear integrable PDE's. arXiv:1104.4268
- Adler, Mark; Orantin, Nicolas; van Moerbeke, Pierre. Universality for the Pearcey process. Phys. D 239 (2010), no. 12, 924--941. MR2639611
- Adler, Mark; van Moerbeke, Pierre. PDEs for the joint distributions of the Dyson, Airy and sine processes. Ann. Probab. 33 (2005), no. 4, 1326--1361. MR2150191 (2006g:60118)
- Adler, Mark; van Moerbeke, Pierre. PDEs for the Gaussian ensemble with external source and the Pearcey distribution. Comm. Pure Appl. Math. 60 (2007), no. 9, 1261--1292. MR2337504 (2009c:82021)
- Aptekarev, Alexander I.; Bleher, Pavel M.; Kuijlaars, Arno B. J. Large $n$ limit of Gaussian random matrices with external source. II. Comm. Math. Phys. 259 (2005), no. 2, 367--389. MR2172687 (2006f:82036)
- Bertola, M.; Cafasso, M. The Riemann-Hilbert approach to the transition between the gap probabilities from the Pearcey to the Airy process. Int. Math. Res. Not. 2011 doi:10.1093/imrn/rnr066
- Bleher, P. M.; Kuijlaars, A. B. J. Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not. 2004, no. 3, 109--129. MR2038771 (2004k:82034)
- Bleher, Pavel; Kuijlaars, Arno B. J. Large $n$ limit of Gaussian random matrices with external source. I. Comm. Math. Phys. 252 (2004), no. 1-3, 43--76. MR2103904 (2005i:82031)
- Bleher, Pavel M.; Kuijlaars, Arno B. J. Large $n$ limit of Gaussian random matrices with external source. III. Double scaling limit. Comm. Math. Phys. 270 (2007), no. 2, 481--517. MR2276453 (2008b:82032)
- Bowick, Mark J.; Brézin, Édouard. Universal scaling of the tail of the density of eigenvalues in random matrix models. Phys. Lett. B 268 (1991), no. 1, 21--28. MR1134369 (92h:82059)
- Brézin, E.; Hikami, S. Correlations of nearby levels induced by a random potential. Nuclear Phys. B 479 (1996), no. 3, 697--706. MR1418841 (97j:82080)
- Brézin, E.; Hikami, S. Level spacing of random matrices in an external source. Phys. Rev. E (3) 58 (1998), no. 6, part A, 7176--7185. MR1662382 (99m:82023)
- Dyson, Freeman J. A Brownian-motion model for the eigenvalues of a random matrix. J. Mathematical Phys. 3 1962 1191--1198. MR0148397 (26 #5904)
- Johansson, Kurt. Discrete polynuclear growth and determinantal processes. Comm. Math. Phys. 242 (2003), no. 1-2, 277--329. MR2018275 (2004m:82096)
- Johansson, Kurt. The arctic circle boundary and the Airy process. Ann. Probab. 33 (2005), no. 1, 1--30. MR2118857 (2005k:60304)
- Moore, Gregory. Matrix models of $2$D gravity and isomonodromic deformation. Random surfaces and quantum gravity (Cargèse, 1990), 157--190, NATO Adv. Sci. Inst. Ser. B Phys., 262, Plenum, New York, 1991. MR1214388
- Okounkov, Andrei; Reshetikhin, Nicolai. Random skew plane partitions and the Pearcey process. Comm. Math. Phys. 269 (2007), no. 3, 571--609. MR2276355 (2008c:60007)
- Prähofer, Michael; Spohn, Herbert. Scale invariance of the PNG droplet and the Airy process. Dedicated to David Ruelle and Yasha Sinai on the occasion of their 65th birthdays. J. Statist. Phys. 108 (2002), no. 5-6, 1071--1106. MR1933446 (2003i:82050)
- Tracy, Craig A.; Widom, Harold. A system of differential equations for the Airy process. Electron. Comm. Probab. 8 (2003), 93--98 (electronic). MR1987098 (2004e:82035)
- Tracy, Craig A.; Widom, Harold. Differential equations for Dyson processes. Comm. Math. Phys. 252 (2004), no. 1-3, 7--41. MR2103903 (2006h:82046)
- Tracy, Craig A.; Widom, Harold. The Pearcey process. Comm. Math. Phys. 263 (2006), no. 2, 381--400. MR2207649 (2006m:82101)
- Zinn-Justin, P. Random Hermitian matrices in an external field. Nuclear Phys. B 497 (1997), no. 3, 725--732. MR1463645 (98k:82100)
- Zinn-Justin, P. Universality of correlation functions of Hermitian random matrices in an external field. Comm. Math. Phys. 194 (1998), no. 3, 631--650. MR1631489 (2000e:82029a)

This work is licensed under a Creative Commons Attribution 3.0 License.