In probability theory, the Wick product, named for Italian physicist Gian-Carlo Wick, is a particular way of defining an adjusted product of a set of random variables. In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a result whose mean is zero.

Dec 11, 2020 · The Wick products of random variables arise through an orthogonalization procedure. Let $f_1,\ldots,f_n$ be (real-valued) random variables on some probability space $ (\Omega,\mathcal {B},\mu)$.

The Wick product was introduced by G.C. Wick in 1950 in the context of quantum field theory. In 1965 T. Hida and N. Ikeda introduced a closely related concept in probability theory.

Aug 27, 2017 · We compute Möbius functions for these posets, and prove a general poset product formula. These provide new proofs and new inversion and product formulas for Wick product versions of Hermite, Chebyshev, Charlier, free Charlier, and Laguerre polynomials.

The Wick product was introduced by C.G. Wick in 1950 [226] as a renor-malization technique in quantum physics. In stochastic analysis this concept, or rather a relative of it, was introduced by Hida and Ikeda in 1967 [101].

Feb 9, 2022 · The Wick product : A1A2A3 A 1 A 2 A 3: is a specific way to order noncommuting operators A1,A2,A3 A 1, A 2, A 3. The concept was introduced by Gian-Carlo Wick in 1950 to avoid "infinite expectation values" that arise from the zero-point-motion of harmonic oscillators.

May 1, 2021 · The purpose of this short note is to describe how the necessity of Wick products comes about, their applications using Feynman diagrams, as well as the utility of Gaussian hypercontractivity theorem.

Jun 5, 2020 · In the book "Gaussian Hilbert Spaces" (Svante Janson) the author introduces the Wick product of a finite sequence of n n random variables living in a Gaussian Hilbert space G G as the orthonormal projection of their product in the n n -th Wiener chaos, namely:

In order to construct the Wick products we introduce the following linear bounded operator in H, Cek = λk ek, k ∈ Zd, where {λk}k∈Zd is a fixed suitable sequence of positive numbers.

The Wick product was introduced by G.C. Wick in 1950 in the context of quantum field theory. In 1965 T. Hida and N. Ikeda introduced a closely related concept in probability theory.