The (q,t)(q,t)-Gaussian process

The (q,t)(q,t)-Fock space Fq,t(H)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 relationaq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=〈f,g〉HtN,aq,t(f)aq,t(g)⁎−qaq,t(g)⁎aq,t(f)=〈f,g〉HtN, 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)⁎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