Spectral properties of partial automorphisms of~a~binary rooted tree
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 280-289.

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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: semigroup, eigenvalues, delta measure.
Mots-clés : partial automorphism, random matrix
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Eugenia Kochubinska. Spectral properties of partial automorphisms of~a~binary rooted tree. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 280-289. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a6/

[1] L. Bartholdi, R. Grigorchuk, “On the Hecke type operators related to some fractal groups”, Proc. Steklov Inst. Math., 231 (2000), 1–41 | MR | Zbl

[2] S. N. Evans, “Eigenvaluse of random wreath products”, Electron. J. Probability, 7:9 (2002), 1–15 | MR

[3] O. Ganyushkin, V. Mazorchuk, Classical Finite Transformation Semigroups. An Introduction, Springer, 2008 | MR

[4] E. Kochubinska, “Combinatorics of partial wreath power of finite inverse symmetric semigroup $\mathcal{IS}_d$”, Algebra Discrete Math., 6:1 (2007), 49–61 | MR

[5] E. Kochubinska, “On cross-sections of partial wreath product of inverse semigroups”, Electron. Notes Discrete Math., 28 (2007), 379–386 | DOI | MR | Zbl

[6] J. D. P. Meldrum, Wreath product of groups and semigroups, Pitman Monographs and Surveys in Pure and Applied Mathematics, 74, Longman Group Ltd., Harlow, 1995 | MR