The (q,t)-Gaussian Process

Blitvic, Natasa (2012) The (q,t)-Gaussian Process. Journal of Functional Analysis, 263 (10). pp. 3270-3305. ISSN 0022-1236

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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.

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Journal Article
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Journal of Functional Analysis
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09 Jan 2017 09:14
Last Modified:
22 Nov 2022 04:15