## Universality of the distribution functions of random matrix theory, preprint

Citations: | 26 - 5 self |

### BibTeX

@MISC{Tracy_universalityof,

author = {Craig A. Tracy and Harold Widom},

title = {Universality of the distribution functions of random matrix theory, preprint},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Dedicated to James B. McGuire on the occasion of his sixty-fifth birthday.

### Citations

1476 |
Exactly solved models in statistical mechanics
- Baxter
(Show Context)
Citation Context ...n or star-triangle equations of McGuire [1], Yang [2] and Baxter [3]. For such models the free energy per site and the one-point correlations in the thermodynamic limit are expressible in closed form =-=[4]-=-. There exists a deep mathematical structure [4, 5] underlying these solvable models; and near critical points, a wider applicability than one would initially expect. This last phenomenon, called univ... |

265 |
Algebraic analysis of solvable lattice models
- Jimbo, Miwa
- 1995
(Show Context)
Citation Context ...g [2] and Baxter [3]. For such models the free energy per site and the one-point correlations in the thermodynamic limit are expressible in closed form [4]. There exists a deep mathematical structure =-=[4, 5]-=- underlying these solvable models; and near critical points, a wider applicability than one would initially expect. This last phenomenon, called universality, has its mathematical roots in the strong ... |

140 |
Random matrics, 2nd ed
- Mehta
- 1991
(Show Context)
Citation Context ...se of the 2D Ising model, the n-point functions (in the scaling limit) are expressible in terms of solutions to integrable differential equations [6, 7, 8]. The Wigner-Dyson theory of random matrices =-=[9, 10]-=- is a second class of statistical models where integrable differential equations and n-point correlations (or more precisely, level-spacing distributions) are related. This paper reviews some of these... |

139 |
Ed.) Statistical Theories of Spectra: Fluctuations
- Porter
- 1965
(Show Context)
Citation Context ...se of the 2D Ising model, the n-point functions (in the scaling limit) are expressible in terms of solutions to integrable differential equations [6, 7, 8]. The Wigner-Dyson theory of random matrices =-=[9, 10]-=- is a second class of statistical models where integrable differential equations and n-point correlations (or more precisely, level-spacing distributions) are related. This paper reviews some of these... |

6 |
de Phys
- Thirumalai, J
- 1995
(Show Context)
Citation Context ...→ 0. (Here K is the operator whose kernel is the sine-kernel acting on L2 (0, s).) The differential equation is the “σ representation” of the PV equation [15, 20]. For other proofs of this result see =-=[21, 22, 16]-=-. 3If Eβ(0; s) denotes the limiting value of ENβ(0; (−t, t)) in the bulk scaling limit with the scaled length of J set equal to s, then [10, 16, 19] E1(0; s) = E2(0; s) = det(I − K+), det(I − K), E4(... |

3 |
in Geometric and quantum aspects of integrable systems (Scheveningen
- Tracy, Widom
- 1992
(Show Context)
Citation Context ...→ 0. (Here K is the operator whose kernel is the sine-kernel acting on L2 (0, s).) The differential equation is the “σ representation” of the PV equation [15, 20]. For other proofs of this result see =-=[21, 22, 16]-=-. 3If Eβ(0; s) denotes the limiting value of ENβ(0; (−t, t)) in the bulk scaling limit with the scaled length of J set equal to s, then [10, 16, 19] E1(0; s) = E2(0; s) = det(I − K+), det(I − K), E4(... |

1 |
in Chen Ning Yang: A Great Physicist of the Twentieth
- Dyson
- 1995
(Show Context)
Citation Context ...→ 0. (Here K is the operator whose kernel is the sine-kernel acting on L2 (0, s).) The differential equation is the “σ representation” of the PV equation [15, 20]. For other proofs of this result see =-=[21, 22, 16]-=-. 3If Eβ(0; s) denotes the limiting value of ENβ(0; (−t, t)) in the bulk scaling limit with the scaled length of J set equal to s, then [10, 16, 19] E1(0; s) = E2(0; s) = det(I − K+), det(I − K), E4(... |

1 |
Application of random matrix theory to quasiperiodic systems, to appear
- unknown authors
- 1996
(Show Context)
Citation Context ...zeros of the Riemann zeta function have given convincing numerical evidence that the normalized consecutive spacings follow the GUE distribution, see Figure 2 (the GUE Hypothesis). Rudnick and Sarnak =-=[34]-=- have proved a restricted form of this hypothesis. 4.2 Eigenvalues of Adjacency Matrices of Quasiperiodic Tilings The discovery of quasicrystals has made the study of statistical mechanical models who... |