Probability Distribution for Coherent Transport of Random Waves

2025/11/06 by Wang, Yunrui, Guo, Cheng · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Optics (physics.optics) #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.04602

Abstract

We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission eigenvalues. We analyze the distribution's shape, bounds, moments, and asymptotic behaviors. In the large n limit, the distribution converges to a Gaussian whose mean and variance depend solely on those of the eigenvalues. This result resolves the apparent paradox between bimodal eigenvalue distribution and unimodal transmissivity distribution.

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