Composition of Gaussian noises from successive convex integrations
Communications on Stochastic Analysis
In the context of isometric imbedding we consider the method of convex integration using Haar functions. Given a short map f0 on [0, 1], under appropriate randomization we construct random isometric maps fn using convex integration. It is then shown that n3/2(fn-f0) converges weakly to a Gaussian noise measure. We next consider the problem of composing the Gaussian noises from successive convex integrations since isometric imbedding for surfaces proceeds through similar steps. Some applications to approximate isometric imbeddings for two dimensional manifolds are also considered.
Dasgupta, Amites, "Composition of Gaussian noises from successive convex integrations" (2018). Journal Articles. 1531.