@article{8603,
  abstract     = {We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.},
  author       = {Frank, Rupert and Seiringer, Robert},
  issn         = {10970312},
  journal      = {Communications on Pure and Applied Mathematics},
  number       = {3},
  pages        = {544--588},
  publisher    = {Wiley},
  title        = {{Quantum corrections to the Pekar asymptotics of a strongly coupled polaron}},
  doi          = {10.1002/cpa.21944},
  volume       = {74},
  year         = {2021},
}

@article{721,
  abstract     = {Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.},
  author       = {Ajanki, Oskari H and Krüger, Torben H and Erdös, László},
  issn         = {00103640},
  journal      = {Communications on Pure and Applied Mathematics},
  number       = {9},
  pages        = {1672 -- 1705},
  publisher    = {Wiley-Blackwell},
  title        = {{Singularities of solutions to quadratic vector equations on the complex upper half plane}},
  doi          = {10.1002/cpa.21639},
  volume       = {70},
  year         = {2017},
}