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Communications in Mathematical Physics

, Volume 156, Issue 2, pp 387–397 | Cite as

The integrated density of states for the difference Laplacian on the modified Koch graph

  • Leonid Malozemov
Article

Abstract

We consider the integrated density of statesN(λ) of the difference Laplacian −Δ on the modified Koch graph. We show thatN(λ) increases only with jumps and a set of jump points ofN(λ) is the set of eigenvalues of −Δ with the infinite multiplicity. We establish also that
$$0< C_1 \leqslant \mathop {\lim }\limits_{\lambda \to 0} \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }}< \overline {\mathop {\lim }\limits_{\lambda \to 0} } \frac{{N(\lambda )}}{{\lambda ^{d_s /2} }} \leqslant C_2< \infty$$
whered s =2log5/log(40/3) is the spectral dimension of MKG.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Spectral Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Leonid Malozemov
    • 1
  1. 1.Department of Applied MathematicsMoscow Civil Engineering InstituteMoscowRussia

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