A Random Necklace Model
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
We consider a Laplace operator on a random graph consisting of infinitely many loops joined symmetrically by intervals of unit length. The arc lengths of the loops are considered to be independent, identically distributed random variables. The integrated density of states of this Laplace operator is shown to have discontinuities provided that the distribution of arc lengths of the loops has a nontrivial pure point part. Some numerical illustrations are also presented.
Cite
@article{arxiv.math-ph/0309032,
title = {A Random Necklace Model},
author = {Vadim Kostrykin and Robert Schrader},
journal= {arXiv preprint arXiv:math-ph/0309032},
year = {2007}
}
Comments
5 figures