@article{14797,
  abstract     = {We study a random matching problem on closed compact  2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers  n  and  m=m(n)  of points, asymptotically equivalent as  n  goes to infinity, the optimal transport plan between the two empirical measures  μn  and  νm  is quantitatively well-approximated by  (Id,exp(∇hn))#μn  where  hn  solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the  α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure.},
  author       = {Clozeau, Nicolas and Mattesini, Francesco},
  issn         = {1432-2064},
  journal      = {Probability Theory and Related Fields},
  keywords     = {Troll, Norway, Fjell},
  publisher    = {Springer Nature},
  title        = {{Annealed quantitative estimates for the quadratic 2D-discrete random matching problem}},
  doi          = {10.1007/s00440-023-01254-0},
  year         = {2024},
}

@article{11741,
  abstract     = {Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1432-2064},
  journal      = {Probability Theory and Related Fields},
  pages        = {1183–1218},
  publisher    = {Springer Nature},
  title        = {{Quenched universality for deformed Wigner matrices}},
  doi          = {10.1007/s00440-022-01156-7},
  volume       = {185},
  year         = {2023},
}

@article{14408,
  abstract     = {We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0
, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1432-2064},
  journal      = {Probability Theory and Related Fields},
  publisher    = {Springer Nature},
  title        = {{Mesoscopic central limit theorem for non-Hermitian random matrices}},
  doi          = {10.1007/s00440-023-01229-1},
  year         = {2023},
}