@article{9318,
  abstract     = {We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N.},
  author       = {Bossmann, Lea and Petrat, Sören P and Seiringer, Robert},
  issn         = {20505094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Asymptotic expansion of low-energy excitations for weakly interacting bosons}},
  doi          = {10.1017/fms.2021.22},
  volume       = {9},
  year         = {2021},
}

@article{9550,
  abstract     = {We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. },
  author       = {Bao, Zhigang and Erdös, László and Schnelli, Kevin},
  issn         = {20505094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Equipartition principle for Wigner matrices}},
  doi          = {10.1017/fms.2021.38},
  volume       = {9},
  year         = {2021},
}

@article{7790,
  abstract     = {We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 .},
  author       = {Deuchert, Andreas and Mayer, Simon and Seiringer, Robert},
  issn         = {20505094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{The free energy of the two-dimensional dilute Bose gas. I. Lower bound}},
  doi          = {10.1017/fms.2020.17},
  volume       = {8},
  year         = {2020},
}

@article{6182,
  abstract     = {We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is
a systematic diagrammatic control of a multivariate cumulant expansion.},
  author       = {Erdös, László and Krüger, Torben H and Schröder, Dominik J},
  issn         = {20505094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Random matrices with slow correlation decay}},
  doi          = {10.1017/fms.2019.2},
  volume       = {7},
  year         = {2019},
}