Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing the sample size have received a lot of attention in recent times. Chernozhukov et al. (Ann. Probab. 45 (2017) 2309–2352) proved Berry–Esseen type result averages class sparsely convex sets including hyperrectangles as special case and they that rate convergence can be upper bounded by $n^{-1/6}$ up...

We consider stochastic wave map equation on real line with solutions taking values in a d-dimensional compact Riemannian manifold. show first that this has unique, global, strong PDE sense, solution local Sobolev spaces. The main result of the paper is proof Large Deviations Principle for case vanishing noise.

This study presents an innovative concept acoustic metrology for on-line dimensional conformance inspection. It investigates the linear and radial dimensions as well as the true position of a center. It conclusively finds that as these dimensions change, the resonant frequencies of tested cylindrical and flat plate parts also shift. The high resonant frequencies appear to shift more than low re...