Given a weakly dependent stationary process, we describe the transition between Berry-Esseen bound and second order Edgeworth expansion in terms of characteristic. This characteristic is sharp: We show that expansions are valid if only certain magnitude. If this not case, still get an optimal bound, thus describing exact transition. also obtain (fractional) given <inline-formula content-type="m...

Abstract In the past decade, differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy. This definition its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition private algorithms or analysing important primitives like amplification by subsampling. Inspired hypothesis testing formulation priv...

We study the convergence rate to normal limit law for the space requirement of random m-ary search trees. While it is known that the random variable is asymptotically normally distributed for 3 ≤ m ≤ 26 and that the limit law does not exist for m > 26, we show that the convergence rate is O(n) for 3 ≤ m ≤ 19 and is O(n), where 4/3 < α < 3/2 is a parameter depending on m for 20 ≤ m ≤ 26. Our app...

Preface The reliable transmission of information bearing signals over a noisy communication channel is at the heart of what we call communication. Information theory—founded by Claude E. Shannon in 1948—provides a mathematical framework for the theory of communication; it describes the fundamental limits to how efficiently one can encode information and still be able to recover it with negligib...