Invariance and Universality Principles for Chaotic Polynomial of Free and Standard Random Variables

Abstract : We present in this report some results about the convergence of the multi-linear homogeneous sums of random variables (also called Chaotic Polynomial), following the invariance principle recently established by Mosset, O'Donnel and Oleszkiewicz [2], the universality principle developed by Nourdin, Pecatti and Reinert in [3] , and the results developed by Déya and Nourdin in the free probability framework [1]. Moreover, we provide au extension of these results by defining an interesting family of these Chaotic Polynomials which have the same but no gaussian or semicircular asymptotically distribution.
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Master thesis
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Ahmed Sid-Ali. Invariance and Universality Principles for Chaotic Polynomial of Free and Standard Random Variables. Mathematics [math]. 2012. ⟨hal-02094906⟩

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