# Investigation of the two-cut phase region in the complex cubic ensemble of random matrices

@article{Barhoumi2022InvestigationOT, title={Investigation of the two-cut phase region in the complex cubic ensemble of random matrices}, author={A. Barhoumi and Pavel Bleher and Alfredo Dea{\~n}o and Maxim L. Yattselev}, journal={Journal of Mathematical Physics}, year={2022} }

We investigate the phase diagram of the complex cubic unitary ensemble of random matrices with the potential [Formula: see text], where t is a complex parameter. As proven in our previous paper [Bleher et al., J. Stat. Phys. 166, 784–827 (2017)], the whole phase space of the model, [Formula: see text], is partitioned into two phase regions, [Formula: see text] and [Formula: see text], such that in [Formula: see text] the equilibrium measure is supported by one Jordan arc (cut) and in [Formula…

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SHOWING 1-10 OF 43 REFERENCES

### Random Matrices and the Six-Vertex Model

- Mathematics
- 2013

This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random…

### Painlevé I double scaling limit in the cubic random matrix model

- Mathematics
- 2013

We obtain the double scaling asymptotic behavior of the recurrence coefficients and the partition function at the critical point of the N × N Hermitian random matrix model with cubic potential. We…

### The isomonodromy approach to matric models in 2D quantum gravity

- Physics
- 1992

AbstractWe consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity associated with the measure exp
$$\sum\limits_{j = 1}^N {t_{j^{Z^{2j,} } } N \geqq 3} $$
. We show…

### Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices

- Mathematics
- 2006

In this paper we derive analytic characterizations for and explicit evaluations of the coefficients of the matrix integral genus expansion. The expansion itself arises from the large N asymptotic…

### Topological Expansion in the Cubic Random Matrix Model

- Mathematics
- 2010

In this paper, we study the topological expansion in the cubic random matrix model, and we evaluate explicitly the expansion coefficients for genus 0 and 1. For genus 0 our formula coincides with the…

### On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight

- Mathematics
- 2016

We study the asymptotics of recurrence coefficients for monic orthogonal polynomials $\pi_n(z)$ with the quartic exponential weight $\exp[-N(\frac 12 z^2+\frac 14 tz^4)]$, where $t\in {\mathbb C}$…

### The Isomonodromy Approach to Matrix Models in 2 D Quantum Gravity

- Physics
- 2004

We consider the double-scaling limit in the hermitian matrix model for N 2D quantum gravity associated with the measure exp £ tjZ\ N^3. We show 7 = 1 that after the appropriate modification of the…