We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and the loss is of squared L2-type. The result from 1980 turned out to be a major step in the theory of nonparametric function estimation.

We show that the class $\\mathscr{B}$, of discrete groups which satisfy conclusion Popa’s cocycle superrigidity theorem for Bernoulli actions, is invariant under measure equivalence. generalize this to setting probability preserving (p.m.p.) groupoids, and as a consequence we deduce any nonamenable lattice in product two noncompact, locally compact second countable must belong $\\mathscr{B}$. a...

In this work we study the problem of secure communication over a fully quantum Gel’fand-Pinsker channel. The best known achievability rate for this channel model in the classical case was proven by Goldfeld, Cuff and Permuter in [1]. We generalize the result of [1]. One key feature of the results obtained in this work is that all the bounds obtained are in terms of error exponent. We obtain our...

In this work we characterize the rate-distortion function of a Wyner-Ziv source, depending on an arbitrarily varying state, known non-causally at the encoder. We then consider the problem of joint source-channel coding of this source transmitted over an arbitrarily varying Gel’fand-Pinsker channel, where we assume that one jammer controls both, the source state sequence and the channel state se...

Abstract Classes of multisorted minions closed under extensions, reflections, and direct powers are considered from a relational point view. As generalization result Barto, Opršal, Pinsker, the closure minion is characterized in terms constructions on relation pairs which invariant for minions.

We prove that if a countable Abelian group A satisfies Thouvenot’s conjecture then for any of its Gaussian actions on a standard Borel space the entropy is either zero or infinity, and moreover, the former case happens iff the spectral measure of the Gaussian action is singular with respect to Haar measure on the dual of A. Introduction. In this note we extend a classical result about the entro...