This article is cited in 1 paper

Large Systems

Interlacing and smoothing: combinatorial aspects

M. L. Blank<sup>ab

a</sup> Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
^b National Research University — Higher School of Economics, Moscow, Russia

Abstract: We study functional consequences of the interlacing property consisting in that a new configuration of “particles” occurs in gaps between elements of a previous configuration. This property was introduced by I. M. Gelfand in terms of spectra of sequences of matrices of increasing dimensions and turned out to be highly needed in many areas of modern mathematics. We examine conditions under which the next generation is “on average smoother” than the previous one and discuss issues related to “complexity” of the set of pairs of interlacing functions.

UDC: 621.391.1+519.1

Received: 22.04.2013
Revised: 23.09.2014

 English version: Problems of Information Transmission, 2014, 50:4, 350–363

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