@article{17281,
  abstract     = {We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.},
  author       = {Campbell, Andrew J and O'Rourke, Sean and Renfrew, David T},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  number       = {13},
  pages        = {10189--10218},
  publisher    = {Oxford University Press},
  title        = {{The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation}},
  doi          = {10.1093/imrn/rnae062},
  volume       = {2024},
  year         = {2024},
}

@article{181,
  abstract     = {We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.},
  author       = {Erdös, László and Krüger, Torben H and Renfrew, David T},
  journal      = {SIAM Journal on Mathematical Analysis},
  number       = {3},
  pages        = {3271 -- 3290},
  publisher    = {Society for Industrial and Applied Mathematics },
  title        = {{Power law decay for systems of randomly coupled differential equations}},
  doi          = {10.1137/17M1143125},
  volume       = {50},
  year         = {2018},
}