An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences
Mathematical Physics
2015-05-20 v1 Statistical Mechanics
math.MP
Probability
Abstract
We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding sequences has an ultrametric structure. Our example provides an illustration of some properties which were suggested to occur for pure states in spin glass models.
Cite
@article{arxiv.1010.2338,
title = {An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences},
author = {Aernout C. D. van Enter and Ellis de Groote},
journal= {arXiv preprint arXiv:1010.2338},
year = {2015}
}