The probability that a character value is zero for the symmetric group

2013/06/05 by Alexander R. Miller, Miller, Alexander R.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.CO #math.GR #math.PR

paper · pdf · doi:10.48550/arxiv.1306.1219

3 pages

arxiv created 2013/06/05 · arxiv updated 2013/06/06

Abstract

We consider random character values X(g) of the symmetric group on n symbols, where X is chosen at random from the set of irreducible characters and g is chosen at random from the group, and we show that X(g)=0 with probability tending to one as n tends to infinity.

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• Central Limit Theorem on the Conjugacy Measure of Symmetric Groups