We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker factor. If G is abelian and the entropy positive, the spectrum is absolutely continuous (Lebesgue co...

This paper treats the Pinsker algebra of a dynamical system in a way which avoids the use of an ordering on the acting group. This enables us to prove some of the classical results about entropy and the Pinsker algebra in the general setup of measure preserving dynamical systems, where the acting group is a discrete countable amenable group. We prove a basic disjointness theorem which asserts t...

In 1957, Chang reported the presence of a substance in the seminal plasma of several mammalian species which had the ability to reverse the capacitation process (decapacitation factor or DF). Bedford & Chang (1962) were partially able to purify DF by ultra-centrifugation. Since that time, a great deal of effort has been given to the purification, isolation and identification of this substance (...

New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verdú for general probability measures. A second bound improves the tightness of an inequality by Csiszár and Talata for arbitrary probability measures that are defined on a common finite set. The latter result is further extended, for probability measures on a ...

appeared in the proceedings of ICDT’10. [44] M. Bodirsky and J. Nešetřil. Constraint satisfaction with countable homogeneous templates. In Proceedings of CSL, pages 44–57, Vienna, 2003. [45] M. Bodirsky and J. Nešetřil. Constraint satisfaction with countable homogeneous templates. Journal of Logic and Computation, 16(3):359–373, 2006. [46] M. Bodirsky and D. Piguet. Finite trees are Ramsey with...

In this paper, a group shift is an expansive action of Zd on a compact metrizable zero dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equalentropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraica...

Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi guessing entropies with respect to either error probability (yielding reverse-Fano Fano inequalities) or total variation distance the uniform reverse-Pinsker Pinsker inequalities). This gives a general picture of how notion randomness can be measured in many areas computer scien...

We generalise the classical Pinsker inequality which relates variational divergence to Kullback-Liebler divergence in two ways: we consider arbitrary f -divergences in place of KL divergence, and we assume knowledge of a sequence of values of generalised variational divergences. We then develop a best possible inequality for this doubly generalised situation. Specialising our result to the clas...