Inference for interacting linear waves in ordered and random media

Abstract

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We investigate systems with both deterministic and quenched disordered couplings on two extreme topologies: complete and sparse graphs. To match further applications in optics also complex couplings and external fields are considered and general inference formulas are derived for real and imaginary parts of Hermitian coupling matrices from real and imaginary parts of complex correlation functions. The whole procedure is, eventually, tested on numerically generated correlation functions and local magnetizations by means of Monte Carlo simulations.

17 pages, 7 figures

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Cited by in corpus (4)

• Statistical mechanics models for multimode lasers and random lasers
• Regularization and decimation pseudolikelihood approaches to statistical inference in $XY$-spin models
• Multi-body quenched disordered $XY$ and $p$-clock models on random graphs
• Improved Pseudolikelihood Regularization and Decimation methods on Non-linearly Interacting Systems with Continuous Variables