J Theor Probab (2017) 30:876–897
Asymptotic Analysis of Symmetric Functions
· A. Naumov
· V. Ulyanov
Received: 25 February 2015 / Revised: 29 January 2016 / Published online: 25 March 2016
© Springer Science+Business Media New York 2016
Abstract In this paper we consider asymptotic expansions for a class of sequences of
symmetric functions of many variables. Applications to classical and free probability
theory are discussed.
Keywords Symmetric functions · Asymptotic expansions · Functional limit
theorems · Edgeworth expansion · U-statistics · Invariance principle
Mathematics Subject Classiﬁcation 60F05 · 60F17
Dedicated to Professor Yuri Prokhorov on the occasion of his 85th birthday (15.12.1929–16.07.2013).
F. Götze was supported by CRC 701 “Spectral Structures and Topological Methods in Mathematics,”
Bielefeld. A. Naumov and V. Ulyanov were supported by RSCF 14-11-00196.
Faculty of Mathematics, Bielefeld University, 33615 Bielefeld, Germany
Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow
Institute for Information Transmission Problems RAS, Moscow 127051, Russia
National Research University Higher School of Economics (HSE), Moscow 101000, Russia