Dec groups for arbitrarily high exponents

On error exponents for arbitrarily varying channels

The minimum probability of error achievable by random codes on the arbitrarily varying channel (AVC) is investigated. New exponential error bounds are found and applied to the AVC with and without input and state constraints. Also considered is a simple subclass of random codes, called randomly modulated codes, in which encoding and decoding operations are separate from code randomization. A un...

Critical Exponents for Groups of Isometries

Let Γ be a convex co-compact group of isometries of a CAT(−1) space X and let Γ0 be a normal subgroup of Γ. We show that, provided Γ is a free group, a sufficient condition for Γ and Γ0 to have the same critical exponent is that Γ/Γ0 is amenable. 0. Introduction and Results Let Γ be a group of isometries acting freely and properly discontinuously on a CAT(−1) space X . Roughly speaking, a CAT(−...

Geometric Exponents and Kleinian Groups

Bell inequalities for arbitrarily high-dimensional systems.

We develop a novel approach to Bell inequalities based on a constraint that the correlations exhibited by local variable theories must satisfy. This is used to construct a family of Bell inequalities for bipartite quantum systems of arbitrarily high dimensionality which are strongly resistant to noise. In particular, our work gives an analytic description of previous numerical results and gener...

Exponents and the Cohomology of Finite Groups

We will provide an example of a p-group G which has elements of order p in some of its integral cohomology groups but which also has the property that p annihilates H̄(G;Z) for all sufficiently high i. This provides a counterexample to a conjecture of A. Adem which stated that if a finite group K has an element of order p in one of its integral cohomology groups then it has such an element in in...