Fourth Moment Theorem and q-Brownian Chaos

Communications in Mathematical Physics

Volumn 321, Issue 1, 2013, Pages 113-134

  Deya, Aurélien ^a   Noreddine, Salim ^b   Nourdin, Ivan ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84878752218     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-012-1631-8     Document Type: Article

References (15)

1. Biane P., Speicher R.: Stochastic calculus with respect to free Brownian motion and analysis on Wigner space. Prob. Th. Rel. Fields 112, 373-409 (1998).
2. Bożejko M., Speicher R.: An example of a generalized Brownian motion. Commun. Math. Phys. 137, 519-531 (1991).
3. Bożejko M., Speicher R.: Interpolations between bosonic and fermionic relations given by generalized Brownian motions. Math. Z. 222, 135-160 (1996).
4. Breuer P., Major P.: Central limit theorems for non-linear functionals of Gaussian fields. J. Mult. Anal. 13, 425-441 (1983).
5. Donati-Martin C.: Stochastic integration with respect to q-Brownian motion. Prob. Th. Rel. Fields 125, 77-95 (2003).
6. Frisch U., Bourret R.: Parastochastics. J. Math. Phys. 11, 364-390 (1970).
7. Greenberg O. W.: Particles with small violations of Fermi or Bose statistics. Phys. Rev. D 43, 4111-4120 (1991).
8. Ismail M. E. H., Stanton D., Viennot G.: The combinatorics of q-Hermite polynomials and the Askey-Wilson integral. Eur. J. Comb. 8(4), 379-392 (1987).
9. Kemp T., Nourdin I., Peccati G., Speicher R.: Wigner chaos and the fourth moment. Ann. Probab. 40(4), 1577-1635 (2011).
10. Nica, A., Speicher, R.: Lectures on the Combinatorics of Free Probability. Cambridge: Cambridge University Press, 2006.
11. Nourdin, I., Peccati, G.: Normal Approximations Using Malliavin Calculus: from Stein's Method to Universality. Cambridge Tracts in Mathematics. Cambridge: Cambridge University Press, 2012.
12. Nualart, D.: The Malliavin calculus and related topics. Berlin: Springer Verlag, Second edition, 2006.
13. Nualart D., Peccati G.: Central limit theorems for sequences of multiple stochastic integrals. Ann. Probab. 33(1), 177-193 (2005).
14. Śniady P.: Gaussian random matrix models for q-deformed Gaussian variables. Commun. Math. Phys. 216, 515-537 (2001).
15. Voiculescu D. V.: Limit laws for random matrices and free product. Invent. Math. 104, 201-220 (1991).