Invariance principles for homogeneous sums of free random variables

Details Invariance principles for homogeneous sums of free random variables Invariance principles for homogeneous sums of free random variables

2012-01-09

arxiv.org/abs/1201.1753v1

Mathematics

Probability

Scientific paper

We extend, in the free probability framework, an invariance principle for multilinear homogeneous sums with low influences recently established in [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low influences: invariance and optimality. {\it Ann. Math.} {\bf 171}, no. 1, 295-341]. To do so, a hypercontractivity property for those homogeneous sums is necessary, and to prove it has turned out to be our main task. Finally, we deduce from our extension several universality phenomenons, in the spirit of the paper [I. Nourdin, G. Peccati and G. Reinert (2010). Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos. {\it Ann. Probab.} {\bf 38}, no. 5, 1947-1985].

Affiliated with

Also associated with

No associations

Rating

Invariance principles for homogeneous sums of free random variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariance principles for homogeneous sums of free random variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariance principles for homogeneous sums of free random variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643256