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The (q,t)-Gaussian Process

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The (q,t)-Gaussian Process. / Blitvic, Natasa.
In: Journal of Functional Analysis, Vol. 263, No. 10, 15.11.2012, p. 3270-3305.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blitvic, N 2012, 'The (q,t)-Gaussian Process', Journal of Functional Analysis, vol. 263, no. 10, pp. 3270-3305. https://doi.org/10.1016/j.jfa.2012.08.006

APA

Blitvic, N. (2012). The (q,t)-Gaussian Process. Journal of Functional Analysis, 263(10), 3270-3305. https://doi.org/10.1016/j.jfa.2012.08.006

Vancouver

Blitvic N. The (q,t)-Gaussian Process. Journal of Functional Analysis. 2012 Nov 15;263(10):3270-3305. Epub 2012 Sept 17. doi: 10.1016/j.jfa.2012.08.006

Author

Blitvic, Natasa. / The (q,t)-Gaussian Process. In: Journal of Functional Analysis. 2012 ; Vol. 263, No. 10. pp. 3270-3305.

Bibtex

@article{ad45fd06b6a94963aaac7e7a327ad330,
title = "The (q,t)-Gaussian Process",
abstract = "The (q,t) -Fock space Fq,t(H) , introduced in this paper, is a deformation of the q-Fock space of Bo{\.z}ejko and Speicher. The corresponding creation and annihilation operators now satisfy the commutation relation aq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=⟨f,g⟩HtN, Turn MathJax off a defining relation of the Chakrabarti–Jagannathan deformed quantum oscillator algebra. The moments of the deformed Gaussian element sq,t(h):=aq,t(h)+aq,t(h)⁎ are encoded by the joint statistics of crossings and nestings in pair partitions. The q=0<t specialization yields a natural single-parameter deformation of the full Boltzmann Fock space of free probability, with the corresponding semicircular measure variously encoded via the Rogers–Ramanujan continued fraction, the t-Airy function, the t-Catalan numbers of Carlitz–Riordan, and the first-order statistics of the reduced Wigner process.",
keywords = "Free probability, q-Gaussians, Fock spaces, Deformed oscillator algebras",
author = "Natasa Blitvic",
year = "2012",
month = nov,
day = "15",
doi = "10.1016/j.jfa.2012.08.006",
language = "English",
volume = "263",
pages = "3270--3305",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "10",

}

RIS

TY - JOUR

T1 - The (q,t)-Gaussian Process

AU - Blitvic, Natasa

PY - 2012/11/15

Y1 - 2012/11/15

N2 - The (q,t) -Fock space Fq,t(H) , introduced in this paper, is a deformation of the q-Fock space of Bożejko and Speicher. The corresponding creation and annihilation operators now satisfy the commutation relation aq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=⟨f,g⟩HtN, Turn MathJax off a defining relation of the Chakrabarti–Jagannathan deformed quantum oscillator algebra. The moments of the deformed Gaussian element sq,t(h):=aq,t(h)+aq,t(h)⁎ are encoded by the joint statistics of crossings and nestings in pair partitions. The q=0<t specialization yields a natural single-parameter deformation of the full Boltzmann Fock space of free probability, with the corresponding semicircular measure variously encoded via the Rogers–Ramanujan continued fraction, the t-Airy function, the t-Catalan numbers of Carlitz–Riordan, and the first-order statistics of the reduced Wigner process.

AB - The (q,t) -Fock space Fq,t(H) , introduced in this paper, is a deformation of the q-Fock space of Bożejko and Speicher. The corresponding creation and annihilation operators now satisfy the commutation relation aq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=⟨f,g⟩HtN, Turn MathJax off a defining relation of the Chakrabarti–Jagannathan deformed quantum oscillator algebra. The moments of the deformed Gaussian element sq,t(h):=aq,t(h)+aq,t(h)⁎ are encoded by the joint statistics of crossings and nestings in pair partitions. The q=0<t specialization yields a natural single-parameter deformation of the full Boltzmann Fock space of free probability, with the corresponding semicircular measure variously encoded via the Rogers–Ramanujan continued fraction, the t-Airy function, the t-Catalan numbers of Carlitz–Riordan, and the first-order statistics of the reduced Wigner process.

KW - Free probability

KW - q-Gaussians

KW - Fock spaces

KW - Deformed oscillator algebras

U2 - 10.1016/j.jfa.2012.08.006

DO - 10.1016/j.jfa.2012.08.006

M3 - Journal article

VL - 263

SP - 3270

EP - 3305

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 10

ER -