Erik Sparre Andersen

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Andersen in Oberwolfach 1963

Erik Sparre Andersen (born December 29, 1919 , † March 8, 2003 ) was a Danish mathematician who dealt with probability theory. The Andersen-Jessen theorem is named after him.

Andersen studied at the University of Copenhagen , where he graduated in 1943 and received his doctorate in 1955. He was a professor at Aarhus University and the Royal Danish Academy of Sciences .

He is known for his Arcsin law of the fluctuation of sums of random variables. The sentence vividly expresses the fact that, contrary to the first impression, it is more likely that the sum of the coin flips (values ​​1, -1 with equal probability) is near the extreme values ​​most of the time instead of the expected value zero. The distribution function is the Arcsin distribution . The theorem had been published by Paul Lévy at Brownscher Movement (1939) and by Mark Kac and Paul Erdős in 1947. Andersen recognized that the theorem was based on a combinatorial principle, which explains its broad applicability. The evidence was later greatly simplified.

Web links

Footnotes

  1. ^ Biographical data according to Who is Who in Scandinavia , 1981, Kong. Danske Videnskab. Selskab releases 2002/03
  2. ↑ Andersen: On the number of positive sums of random variables. In: Skand. Actuary Tidskrift. Volume 32, 1949, pp. 27-36; On sums of symmetrically dependent random variables. In: Skand. Actuary Tidskrift. Volume 36, 1953, pp. 123-138; Fluctuations of sums of random variables. In: Mathematica Scandinavica. Volume 1, 1953, pp. 263-285; Volume 2, 1954, pp. 195-223. Illustrated for example in William Feller : Introduction to probability theory and its applications. Volume 1, Chapter III / 4; Konrad Jacobs (editor and author): Selecta Mathematica. Volume 1. Springer, 1969; Jacobs: Discrete Stochastics. Birkhäuser, 1992
  3. ↑ Compositio Mathematica, Volume 7, p. 283
  4. ^ Bull. AMS. Volume 53, p. 1011
personal data
SURNAME Andersen, Erik Sparre
BRIEF DESCRIPTION Danish mathematician
DATE OF BIRTH December 29, 1919
DATE OF DEATH March 8, 2003