@article{6232,
abstract = {The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly—and in a sense, arbitrarily—bad: as shown by Krylov[ SIAM J. Math. Anal.34(2003) 1167–1182], for any α>0 one can find a simple 1-dimensional constant coefficient linear equation whose solution at the boundary is not α-Hölder continuous.We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are proved to be α-Hölder continuous up to the boundary with some α>0.},
author = {Gerencser, Mate},
issn = {00911798},
journal = {Annals of Probability},
number = {2},
pages = {804--834},
publisher = {Institute of Mathematical Statistics},
title = {{Boundary regularity of stochastic PDEs}},
doi = {10.1214/18-AOP1272},
volume = {47},
year = {2019},
}
@article{6511,
abstract = {Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).},
author = {Bao, Zhigang and Erdös, László and Schnelli, Kevin},
issn = {00911798},
journal = {Annals of Probability},
number = {3},
pages = {1270--1334},
publisher = {Institute of Mathematical Statistics},
title = {{Local single ring theorem on optimal scale}},
doi = {10.1214/18-AOP1284},
volume = {47},
year = {2019},
}