This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost bi-Lipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but ‘almost homogeneous’. We therefore study the problem of embedding an almost homogeneous subset ...

Abstract We consider homogeneous open quantum walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of trajectories walk. prove that properly rescaled asymptotically approaches mixture Gaussian measures. can generalize existing central limit type results give more explicit expressions for involved asymptotic quantities, dropping any addit...

We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space ΞB contained in the space of bounded Borel measures on T in such a way that the map B → ΞB defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of a...

The Khinchin–Kahane inequality is a fundamental result in the probability literature, with most general version to date holding Banach spaces. Motivated by modern settings and applications, we generalize this arbitrary metric groups which are abelian. If instead of abelian one assumes group's be norm (i.e., Z>0-homogeneous), then explain how improves same as This occurs via “transfer principle”...