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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2018, Volume 26, Issue 2, Pages 280–289 (Mi adm684)

RESEARCH ARTICLE

Spectral properties of partial automorphisms of a binary rooted tree

Eugenia Kochubinska

Taras Shevchenko National University of Kyiv, Volodymyrska, 64, 01601, Kiev, Ukraine

Abstract: We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism $x$ we assign its action matrix $A_x$. It is shown that the uniform distribution on eigenvalues of $A_x$ converges weakly in probability to $\delta_0$ as $n \to \infty$, where $\delta_0$ is the delta measure concentrated at $0$.

Keywords: partial automorphism, semigroup, eigenvalues, random matrix, delta measure.

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MSC: 20M18, 20M20, 5C05
Revised: 17.12.2017
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Citation: Eugenia Kochubinska, “Spectral properties of partial automorphisms of a binary rooted tree”, Algebra Discrete Math., 26:2 (2018), 280–289

Citation in format AMSBIB
\Bibitem{Koc18} \by Eugenia~Kochubinska \paper Spectral properties of partial automorphisms of~a~binary rooted tree \jour Algebra Discrete Math. \yr 2018 \vol 26 \issue 2 \pages 280--289 \mathnet{http://mi.mathnet.ru/adm684}