A Random Necklace Model

Details A Random Necklace Model A Random Necklace Model

2003-09-12

arxiv.org/abs/math-ph/0309032v1

Waves in Random Media 14 (2004), S75 - S90

Physics

Mathematical Physics

5 figures

Scientific paper

10.1088/0959-7174/14/1/012

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.

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