A random necklace model

2003/09/12 by Vadim Kostrykin, Robert Schrader · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math-ph #math.MP #msc:34B45 #msc:60H25

paper · pdf · doi:10.1088/0959-7174/14/1/012

published as Waves in Random Media 14 (2004), S75 - S90 · 5 figures

arxiv created 2003/09/12 · openalex publication_date 2004/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dedicated to Elliott Lieb on occasion of his 70-th birthday 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. 1.

Citations

• Kirchhoff's rule for quantum wires
• The generalized star product and the factorization of scattering matrices on graphs
• Quantum Wires with Magnetic Fluxes
• Global bounds for the Lyapunov exponent and the integrated density of states of random Schrödinger operators in one dimension
• SCATTERING THEORY APPROACH TO RANDOM SCHRÖDINGER OPERATORS IN ONE DIMENSION

Cited by

• Anderson Localization for radial tree-like random quantum graphs

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