@article{11354,
  abstract     = {We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.},
  author       = {Dello Schiavo, Lorenzo},
  issn         = {2168-894X},
  journal      = {Annals of Probability},
  number       = {2},
  pages        = {591--648},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold}},
  doi          = {10.1214/21-AOP1541},
  volume       = {50},
  year         = {2022},
}

@article{11418,
  abstract     = {We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N
Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {2168-894X},
  journal      = {Annals of Probability},
  number       = {3},
  pages        = {984--1012},
  publisher    = {Institute of Mathematical Statistics},
  title        = {{Normal fluctuation in quantum ergodicity for Wigner matrices}},
  doi          = {10.1214/21-AOP1552},
  volume       = {50},
  year         = {2022},
}