A Peccati-Tudor type theorem for Rademacher chaoses

In this article, we prove that in the Rademacher setting, a random vector with chaotic components is close in distribution to a centered Gaussian vector, if both the maximal influence of the associated kernel and the fourth cumulant of each component is small. In particular, we recover the univariate case recently established in Döbler and Krokowski (2019). Our main strategy consists in a novel adaption of the exchangeable pairs couplings initiated in Nourdin and Zheng (2017), as well as its combination with estimates via chaos decomposition.

The q-Gamma White Noise

For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γα,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L2 space with respect to the measure γα,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.

Generalized free Gaussian white noise

<p>Based on an adequate new Gel'fand triple, we construct the infinite dimensional free Gaussian white noise measure \(\mu\) using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an \(L^{2}\) space with respect to the measure \(\mu\).</p>

Polymer measure: Varadhan's renormalization revisited

Through chaos decomposition, we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.