Singular vectors under random perturbation

Singular Vector Perturbation Under Gaussian Noise

We perform a non-asymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can be used to facilitate the error analysis in linear dimension reduction.

The 3d Quasigeostrophic Equation under Random Perturbation

The three-dimensional baroclinic quasigeostrophic ow model has been widely used to study basic mechanisms in oceanic ows and climate dynamics. In this paper, we consider this ow model under random wind forcing and time-periodic uctuations on uid boundary (the interface between the oceans and the atmosphere). The time-periodic uctuations are due to periodic rotation of the earth and thus periodi...

Persistent Homoclinic Orbits for Nonlinear Schrödinger Equation Under Singular Perturbation

Existence of homoclinic orbits in the cubic nonlinear Schrödinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup eǫt∂ 2 x at ǫ = 0. This article is a substantial generalization of [3], and motivated by the effort of Dr. Zeng [9] [8]. The mistake of Zeng in [8] is corrected with a normal form transform approach. Both one and two unstable ...

Singular solution of the Liouville equation under perturbation

is considered. We are interesting for asymptotics of the perturbed solution u(x, t; ε) as ε→ 0. Perturbation theory for integrable equations remains a very attractive task. As a rule a perturbation of smooth solutions such as a single soliton were usually considered. We intend here to discuss a perturbation of a singular solution under assumption that the perturbed solution has singularities as...

Autoregressive Gaussian Random Vectors of First Order