@article{12290,
  abstract     = {We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  keywords     = {Statistics, Probability and Uncertainty, Statistics and Probability},
  pages        = {1--38},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Optimal multi-resolvent local laws for Wigner matrices}},
  doi          = {10.1214/22-ejp838},
  volume       = {27},
  year         = {2022},
}

@article{10285,
  abstract     = {We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur.},
  author       = {Dubach, Guillaume},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{On eigenvector statistics in the spherical and truncated unitary ensembles}},
  doi          = {10.1214/21-EJP686},
  volume       = {26},
  year         = {2021},
}

@article{8973,
  abstract     = {We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity.},
  author       = {Redig, Frank and Saada, Ellen and Sau, Federico},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  publisher    = { Institute of Mathematical Statistics},
  title        = {{Symmetric simple exclusion process in dynamic environment: Hydrodynamics}},
  doi          = {10.1214/20-EJP536},
  volume       = {25},
  year         = {2020},
}

@article{6359,
  abstract     = {The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.},
  author       = {Dareiotis, Konstantinos and Gerencser, Mate},
  issn         = {1083-6489},
  journal      = {Electronic Journal of Probability},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift}},
  doi          = {10.1214/20-EJP479},
  volume       = {25},
  year         = {2020},
}