# Critical measures for vector energy: Global structure of trajectories of quadratic differentials

@article{MartnezFinkelshtein2015CriticalMF, title={Critical measures for vector energy: Global structure of trajectories of quadratic differentials}, author={Andrei Mart{\'i}nez-Finkelshtein and Guilherme L. F. Silva}, journal={Advances in Mathematics}, year={2015}, volume={302}, pages={1137-1232} }

## 9 Citations

### Global‐phase portrait and large‐degree asymptotics for the Kissing polynomials

- MathematicsStudies in Applied Mathematics
- 2021

We study a family of monic orthogonal polynomials that are orthogonal with respect to the varying, complex‐valued weight function, exp(nsz) , over the interval [−1,1] , where s∈C is arbitrary. This…

### Critical measures for vector energy: Asymptotics of non-diagonal multiple orthogonal polynomials for a cubic weight

- MathematicsAdvances in Mathematics
- 2019

### Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Pad\'e Approximants and Asymptotics

- Mathematics
- 2019

Given $K$ arbitrary poles, which are neither necessarily distinct nor bounded, on the extended real line, a corresponding ordered base of rational functions orthogonal with respect to varying…

### Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials

- MathematicsConstructive Approximation
- 2022

For a given polynomial P with simple zeros, and a given semiclassical weight w, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an…

### Do Orthogonal Polynomials Dream of Symmetric Curves?

- MathematicsFound. Comput. Math.
- 2016

Some “mysterious” configurations of zeros of polynomials, defined by an orthogonality condition with respect to a sum of exponential functions on the plane, that appeared as a results of the numerical experiments are discussed.

### Do Orthogonal Polynomials Dream of Symmetric Curves?

- MathematicsFoundations of Computational Mathematics
- 2016

The complex or non-Hermitian orthogonal polynomials with analytic weights are ubiquitous in several areas such as approximation theory, random matrix models, theoretical physics and in numerical…

### The Mother Body Phase Transition in the Normal Matrix Model

- Mathematics
- 2016

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential…

### Spectral Curves, Variational Problems and the Hermitian Matrix Model with External Source

- MathematicsCommunications in Mathematical Physics
- 2021

We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied…

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