@article{12232,
  abstract     = {We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1424-0661},
  journal      = {Annales Henri Poincaré},
  keywords     = {Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics},
  number       = {11},
  pages        = {3981--4002},
  publisher    = {Springer Nature},
  title        = {{Density of small singular values of the shifted real Ginibre ensemble}},
  doi          = {10.1007/s00023-022-01188-8},
  volume       = {23},
  year         = {2022},
}

@article{9912,
  abstract     = {In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries.},
  author       = {Erdös, László and Krüger, Torben H and Nemish, Yuriy},
  issn         = {1424-0661},
  journal      = {Annales Henri Poincaré },
  pages        = {4205–4269},
  publisher    = {Springer Nature},
  title        = {{Scattering in quantum dots via noncommutative rational functions}},
  doi          = {10.1007/s00023-021-01085-6},
  volume       = {22},
  year         = {2021},
}

@article{6788,
  abstract     = {We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations.},
  author       = {Leopold, Nikolai K and Petrat, Sören P},
  issn         = {1424-0661},
  journal      = {Annales Henri Poincare},
  number       = {10},
  pages        = {3471–3508},
  publisher    = {Springer Nature},
  title        = {{Mean-field dynamics for the Nelson model with fermions}},
  doi          = {10.1007/s00023-019-00828-w},
  volume       = {20},
  year         = {2019},
}