作者：Chatterjee, Sourav; Dunlap, Alexander
作者单位：Stanford University; Stanford University
摘要：The (d + 1)-dimensional KPZ equation is the canonical model for the growth of rough d-dimensional random surfaces. A deep mathematical understanding of the KPZ equation for d = 1 has been achieved in recent years, and the case d >= 3 has also seen some progress. The most physically relevant case of d = 2, however, is not very well understood mathematically, largely due to the renormalization that is required: in the language of renormalization group analysis, the d = 2 case is neither ultravio...
作者：Campese, Simon; Nourdin, Ivan; Nualart, David
作者单位：University of Luxembourg; University of Kansas
摘要：Let Y = (Y(t))(t >= 0) be a zero-mean Gaussian stationary process with covariance function rho : R -> R satisfying rho (0) = 1. Let f : R -> R be a square-integrable function with respect to the standard Gaussian measure, and suppose the Hermite rank of f is d >= 1. If integral(R) vertical bar rho(s)vertical bar(d) ds < infinity, then the celebrated Breuer-Major theorem (in its continuous version) asserts that the finite-dimensional distributions of Z(epsilon) := root epsilon integral(./epsilo...
