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A Note on Invariant Random Variables

Abstract : In this paper we present a simple theory, based on the notion of group action on a set, which explains why processes of throwing random sets of points and throwing random lines are similar up to the second moment of counting functions connected with them. We also discuss other applications of this method and show how to calculate higher moments using the group acting on a set.
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Jacek Cichoń, Marek Klonowski. A Note on Invariant Random Variables. 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), 2010, Vienna, Austria. pp.107-116. ⟨hal-01185584⟩

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