A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups
Abstract
This paper introduces a (2+1)-dimensional Gaussian field which has the Gaussian free field on the upper half-plane with zero boundary conditions as certain two-dimensional sections. Along these sections, called space-like paths, it matches the Gaussian field from eigenvalues of random matrices and from a growing random surface. However, along time-like paths the behavior is different. The Gaussian field arises as the asymptotic fluctuations in quantum random walks on quantum groups U_q(gl_n). This quantum random walk is a q-deformation of previously considered quantum random walks. When restricted to the space-like paths, the moments of the quantum random walk match the moments of the growing random surface.
Keywords
Cite
@article{arxiv.1601.04402,
title = {A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups},
author = {Jeffrey Kuan},
journal= {arXiv preprint arXiv:1601.04402},
year = {2023}
}
Comments
version 2 improves the exposition and fills in a gap in the proof