Displaying similar documents to “Non-commutative probability limit theorems”

Probability of reversal in an election with more than two candidates.

Vijay K. Rohatgi (1982)

Trabajos de Estadística e Investigación Operativa

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Consider an election with three candidates A, A and A. Suppose that N is the total number of votes cast of which A receives a votes, A receives a votes and A receives a = N - (a + a) votes. We assume without loss of generality that a > a > a. Suppose further that n votes are irregular or suspect. If these votes are removed it is possible that the result of the election may be reversed. Does such a possibility preclude the determination of the rightful winner without holding...

On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions

Florent Benaych-Georges (2010)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we prove a result linking the square and the rectangular -transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.