Bernoulli

  • Bernoulli
  • Volume 20, Number 2 (2014), 586-603.

Invariance principles for homogeneous sums of free random variables

Aurélien Deya and 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.

Article information

Source
Bernoulli, Volume 20, Number 2 (2014), 586-603.

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393593998

Digital Object Identifier
doi:10.3150/12-BEJ498

Mathematical Reviews number (MathSciNet)
MR3178510

Zentralblatt MATH identifier
1292.60041

Keywords
central limit theorems chaos free Brownian motion free probability homogeneous sums Lindeberg principle universality Wigner chaos

Citation

Deya, Aurélien; Nourdin, Ivan. Invariance principles for homogeneous sums of free random variables. Bernoulli 20 (2014), no. 2, 586--603. doi:10.3150/12-BEJ498. https://projecteuclid.org/euclid.bj/1393593998


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References

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