One-dimensional discrete Gaussian Markov processes: Harmonic decomposition of invariant boundary conditions
Probability
2023-05-31 v1
Abstract
We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non trivial basis from the study of a meromorphic matrix-valued function (inherent to the model) and its singularities. This provides a simple algorithm for the explicit computation of invariant measures. As an application, we give an "eigen" version of Szeg\H{o} limit theorem for matrix valued trigonometric polynomials.
Keywords
Cite
@article{arxiv.2305.18892,
title = {One-dimensional discrete Gaussian Markov processes: Harmonic decomposition of invariant boundary conditions},
author = {Emilien Bodiot},
journal= {arXiv preprint arXiv:2305.18892},
year = {2023}
}