The Spectrum of an Adelic Markov Operator
Spectral Theory
2013-05-29 v1 Number Theory
Abstract
With the help of the representation of SL(2,Z) on the rank two free module over the integer adeles, we define the transition operator of a Markov chain. The real component of its spectrum exhibits a gap, whereas the non-real component forms a circle of radius 1/\sqrt{2}.
Cite
@article{arxiv.1305.6410,
title = {The Spectrum of an Adelic Markov Operator},
author = {Andreas Knauf},
journal= {arXiv preprint arXiv:1305.6410},
year = {2013}
}
Comments
38 pages, 5 figures