# Four-Dimensional Painlevé-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems

@article{Kawakami2017FourDimensionalPE, title={Four-Dimensional Painlev{\'e}-Type Equations Associated with Ramified Linear Equations III: Garnier Systems and Fuji-Suzuki Systems}, author={Hiroshi Kawakami}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2017}, volume={13}, pages={096} }

This is the last part of a series of three papers entitled "Four-dimensional Painlev\'e-type equations associated with ramified linear equations". In this series of papers we aim to construct the complete degeneration scheme of four-dimensional Painlev\'e-type equations. In the present paper, we consider the degeneration of the Garnier system in two variables and the Fuji-Suzuki system.

## 14 Citations

### Four-dimensional Painlev\'e-type equations associated with ramified linear equations II: Sasano systems

- Mathematics
- 2016

This is a continuation of the paper "Four-dimensional Painleve-type equations associated with ramified linear equations I: Matrix Painleve systems" (arXiv:1608.03927). In this series of three papers…

### Four-dimensional Painlev\'e-type equations associated with ramified linear equations I: Matrix Painlev\'e systems

- Mathematics
- 2016

As a sequel to [16], this series of three papers constructs the complete degeneration scheme of four-dimensional Painlevé-type equations which includes the Painlevé-type equations associated with…

### Four-dimensional Painlev\'e-type difference equations

- Mathematics
- 2018

We focus on Fuchsian equations with four accessory parameters and three singular points. We see that the Fuchsian equations admit a "degeneration scheme" in some sense, which is expected to give rise…

### Uniqueness of Polarization for the Autonomous 4-dimensional Painlevé-type Systems

- MathematicsInternational Mathematics Research Notices
- 2020

We prove that for any autonomous 4-dimensional integral system of Painlevé type, the Jacobian of the generic spectral curve has a unique polarization, and thus by Torelli’s theorem cannot be…

### Noncommutative Painlevé Equations and Systems of Calogero Type

- MathematicsCommunications in Mathematical Physics
- 2018

All Painlevé equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction of Calogero type…

### Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System

- MathematicsCommunications in Mathematical Physics
- 2018

We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of…

### Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System

- MathematicsCommunications in Mathematical Physics
- 2018

We study Fredholm determinants of the Painlevé II and Painlevé XXXIV kernels. In certain critical unitary random matrix ensembles, these determinants describe special gap probabilities of…

### Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systems

- MathematicsStudies in Applied Mathematics
- 2020

We consider the Hankel determinant generated by the Gaussian weight with two jump discontinuities. Utilizing the results of Min and Chen [Math. Methods Appl Sci. 2019;42:301‐321] where a second‐order…

### Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems

- MathematicsNonlinearity
- 2021

We study the orthogonal polynomials and the Hankel determinants associated with the Gaussian weight with two jump discontinuities. When the degree n is finite, the orthogonal polynomials and the…

### Singular Values of Products of Ginibre Random Matrices

- Mathematics
- 2016

The squared singular values of the product of M complex Ginibre matrices form a biorthogonal ensemble, and thus their distribution is fully determined by a correlation kernel. The kernel permits a…

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This is a continuation of the paper "Four-dimensional Painleve-type equations associated with ramified linear equations I: Matrix Painleve systems" (arXiv:1608.03927). In this series of three papers…

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