Events Archive

Stochastisches Kolloquium

Mittwoch, 30. Oktober 2019, 14:15 Uhr in Raum 903:

Hsien-Kuei Hwang (Academia Sinica, Taipei)

Title: Stirling numbers of the second kind: the history of early developments and an elementary approach to asymptotic normality

Abstract: A historical account is given of the early developments of
the Stirling numbers of the second kind: in contrast to those in the West,
those in the East, notably in Japan, have remained mostly unknown
with the corresponding combinatorial origin traced back to at least 1600.
I will talk about the background, the mathematical developments in Japan in the
Edo Period (1603--1868), and the corresponding developments in the West.
Then after a brief survey on the various methods for proving the asymptotic normality
N(n/log n, n/(log n)^{^2}) of the Stirling numbers of the second kind, I will introduce
a very simple, elementary approach to proving the local and central limit theorems.
The approach, based on the principle of inclusion and exclusion and
Stirling's formula for the factorial, is also applicable to several dozens of other
examples in the literature and in the OEIS (Online Encyclopedia of Integer Sequences).

This talk is based on joint works with Xiaoling Dou (Waseda University) and
with Chong-Yi Li (Academia Sinica).