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Probl. Peredachi Inf., 2012, Volume 48, Issue 3, Pages 96–110 (Mi ppi2089)  

Large Systems

Fine structure of a one-dimensional discrete point system

V. A. Malyshev

Laboratory of Large Random Systems, Faculty of Mathematics and Mechanics, Lomonosov Moscow State University

Abstract: We consider a system of $N$ points $x_1<…<x_N$ on a segment of the real line. An ideal system (crystal) is a system where all distances between neighbors are the same. Deviation from idealness is characterized by a system of finite differences $\nabla_i^1=x_{i+1}-x_i$, $\nabla_i^{k+1}=\nabla_{i+1}^k-\nabla_i^k$, for all possible $i$ and $k$. We find asymptotic estimates as $N\to\infty$, $k\to\infty$, for a system of points minimizing the potential energy of a Coulomb system in an external field.

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English version:
Problems of Information Transmission, 2012, 48:3, 283–296

Bibliographic databases:

Document Type: Article
UDC: 621.391.1+519.2
Received: 30.11.2011
Revised: 28.05.2012

Citation: V. A. Malyshev, “Fine structure of a one-dimensional discrete point system”, Probl. Peredachi Inf., 48:3 (2012), 96–110; Problems Inform. Transmission, 48:3 (2012), 283–296

Citation in format AMSBIB
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\by V.~A.~Malyshev
\paper Fine structure of a~one-dimensional discrete point system
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 3
\pages 96--110
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\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 3
\pages 283--296
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