Birch's theorem with shifts

Brooks’ theorem for Bernoulli shifts

If Γ is an infinite group with finite symmetric generating set S, we consider the graph G(Γ, S) on [0, 1]Γ by relating two distinct points if an element of s sends one to the other via the shift action. We show that, aside from the cases Γ = Z and Γ = (Z/2Z) ∗ (Z/2Z), G(Γ, S) satisfies a measure-theoretic version of Brooks’ theorem: there is a G(Γ, S)-invariant conull Borel set B ⊆ [0, 1]Γ and ...

Girsanov theorem for anticipative shifts on Poisson space

We study the absolute continuity of the image measure of the canonical Poisson probability measure under nonlinear shifts. The Radon-Nykodim density function is expressed using a Carleman-Fredholm determinant and a divergence operator. Results are obtained for non-necessarily invertible transformations, under almost-sure differentiability hypothesis.

The Decomposition Theorem For Two-Dimensional Shifts Of Finite Type

A one-dimensional shift of finite type can be described as the collection of bi-infinite “walks” along an edge graph. The Decomposition Theorem states that every conjugacy between two shifts of finite type can be broken down into a finite sequence of splittings and amalgamations of their edge graphs. When dealing with two-dimensional shifts of finite type, the appropriate edge graph description...

A central limit theorem for functions of a Markov chain with applications to shifts

Asymptotic phase shifts and Levinson theorem for 2D potentials with inverse square singularities

Franz G. Mertens Physikalisches Institut, Universität Bayreuth, D–95440 Bayreuth, Germany (Dated: November 11, 2002) Abstract The Levinson theorem for two–dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m–th partial wave is related to the phase shift and the singularity strength of the potential. For ...