Exact equivalences and phase discrepancies between random matrix ensembles

Abstract

We study two types of random matrix ensembles that emerge when considering the same probability measure on partitions. One is the Meixner ensemble with a hard wall and the other are two families of unitary matrix models, with weight functions that can be interpreted as characteristic polynomial insertions. We show that the models, while having the same exact evaluation for fixed values of the parameter, may present a different phase structure. We find phase transitions of the second and third order, depending on the model. Other relationships, via direct mapping, between the unitary matrix models and continuous random matrix ensembles on the real line, of Cauchy-Romanovski type, are presented and studied both exactly and asymptotically. The case of orthogonal and symplectic groups is studied as well and related to Wronskians of Chebyshev polynomials, that we evaluate at large $N$.

41 pages, 10 figures. v2: some explanations and references added, final version

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Cited by in corpus (8)

• Phases of five-dimensional supersymmetric gauge theories
• Unitary matrix models and random partitions: Universality and multi-criticality
• Multiple phases in a generalized Gross-Witten-Wadia matrix model
• Deformed Cauchy random matrix ensembles and large $N$ phase transitions
• Phases of unitary matrix models and lattice QCD2
• Dynamical quantum phase transitions from random matrix theory
• Crystal bases and three-dimensional $\mathcal{N}=4$ Coulomb branches
• Schur expansion of random-matrix reproducing kernels