The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model
Mathematical Physics
2017-09-21 v1 math.MP
Abstract
We consider the adjacency matrix associated with a graph that describes transitions between states of the discrete Preisach memory model. This matrix can also be associated with the last-in-first-out inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil's staircase. The eigenvectors of the adjacency matrix are also expressed analytically.
Keywords
Cite
@article{arxiv.1709.06960,
title = {The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model},
author = {Tamas Kalmar-Nagy and Andreas Amann and Daniel Kim and Dmitrii Rachinskii},
journal= {arXiv preprint arXiv:1709.06960},
year = {2017}
}