A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups

2016/01/18 by Kuan, Jeffrey
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1601.04402

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.

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