@article{21472,
  abstract     = {We study the ground state energy of a gas of spin 1/2 fermions with repulsive short-range interactions. We derive an upper bound that agrees, at low density e, with the Huang–Yang conjecture. The latter captures the first three terms in an asymptotic low-density expansion, and in particular the Huang–Yang correction term of order e^7/3. Our trial state is constructed using an adaptation of the bosonic Bogoliubov theory to the Fermi system, where the correlation structure of fermionic particles is incorporated by quasi-bosonic Bogoliubov transformations. In the latter, it is important to consider a modified zero-energy scattering equation that takes into account the presence of the Fermi sea, in the spirit of the Bethe–Goldstone equation.},
  author       = {Giacomelli, Emanuela L. and Hainzl, Christian and Nam, Phan Thành and Seiringer, Robert},
  issn         = {1097-0312},
  journal      = {Communications on Pure and Applied Mathematics},
  publisher    = {Wiley},
  title        = {{The Huang–Yang formula for the low-density Fermi gas: Upper bound}},
  doi          = {10.1002/cpa.70040},
  year         = {2026},
}

@article{15378,
  abstract     = {We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest.},
  author       = {Erdös, László and Ji, Hong Chang},
  issn         = {1097-0312},
  journal      = {Communications on Pure and Applied Mathematics},
  number       = {9},
  pages        = {3785--3840},
  publisher    = {Wiley},
  title        = {{Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices}},
  doi          = {10.1002/cpa.22201},
  volume       = {77},
  year         = {2024},
}

@article{10405,
  abstract     = {We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. },
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1097-0312},
  journal      = {Communications on Pure and Applied Mathematics},
  number       = {5},
  pages        = {946--1034},
  publisher    = {Wiley},
  title        = {{Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices}},
  doi          = {10.1002/cpa.22028},
  volume       = {76},
  year         = {2023},
}

@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         = {1097-0312},
  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},
}