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An asymptotic distribution theory for Eulerian recurrences


Academic Report

Title: An asymptotic distribution theory for Eulerian recurrences

Reporter: HUANG Xiangui (Institute of Statistics, Taiwan Central Research Institute)

Time: November 17, 2017(Friday) PM 13:30-14:30

Location: A#1101 room, Innovation Park Building

Contact: Prof. WANG Yi (tel: 84708351-8128)

Abstract: We discuss linear recurrences of Eulerian type of the form                                                                                             , with  given, where a  and c  are in most cases polynomials of low degree. We characterize the various limit laws of the coefficients of  for large n using the method of moments and analytic combinatorial tools under varying a  and c  . We apply our results to more than two hundreds of concrete examples that we collected from the literature and from Sloane's Online Encyclopedia of Integer Sequences. Not only most of the limit results are new, but they are unified in the same framework. The limit laws we worked out include normal, half-normal, Rayleigh, beta, Poisson,

negative binomial, Mittag-Leffler, Bernoulli, etc., showing the richness and diversity of such a simple recurrence scheme, as well as the generality and power of the approaches used.

The brief introduction to the reporter: Huang Xiangui achieved his Ph.D. in Integrated Polytechnic University, Paris, France in December 1994. Now he is a  researcher of Institute of Statistics, National Taiwan Academy of Sciences. The research interests are applied probability theory, algorithm analysis, asymptotic analysis. In 2003, he won the Bessel Research Award of the German Humboldt Foundation; In 2013, he won the Taiwan Affairs Science and Technology Prize and the Ministry of Education Academic Award.