Phase Transitions and Equilibrium Measures in Random Matrix Models

@article{MartnezFinkelshtein2013PhaseTA,
  title={Phase Transitions and Equilibrium Measures in Random Matrix Models},
  author={Andrei Mart{\'i}nez-Finkelshtein and Ram'on Orive and Evguenii Rakhmanov},
  journal={Communications in Mathematical Physics},
  year={2013},
  volume={333},
  pages={1109-1173}
}
The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial external field. The total mass of the measure is considered as the main parameter, which may be interpreted also either as temperature or time. Our main tools are differentiation formulas with respect to the parameters of the problem, and a representation of the… 
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