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2014•BernoulliOpen access

Invariance principles for homogeneous sums of free random variables

Aurélien Deya, Ivan Nourdin

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Abstract

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established by Mossel, O’Donnel and Oleszkiewicz in [Ann. of Math. (2) 171 (2010) 295–341]. We then deduce several universality phenomenons, in the spirit of the paper [Ann. Probab. 38 (2010) 1947–1985] by Nourdin, Peccati and Reinert.

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We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established by Mossel, O’Donnel and Oleszkiewicz in [Ann. of Math. (2) 171 (2010) 295–341]. We then deduce several universality phenomenons, in the spirit of the paper [Ann. Probab. 38 (2010) 1947–1985] by Nourdin, Peccati and Reinert.

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Available abstract

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established by Mossel, O’Donnel and Oleszkiewicz in [Ann. of Math. (2) 171 (2010) 295–341]. We then deduce several universality phenomenons, in the spirit of the paper [Ann. Probab. 38 (2010) 1947–1985] by Nourdin, Peccati and Reinert.

Key concepts: Mathematics, Universality (dynamical systems), Homogeneous, Multilinear map, Gaussian, Invariance principle, Homogeneous function, Pure mathematics

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