Geodesic
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 
@article{ADM_2018_26_2_a6,
     author = {Eugenia Kochubinska},
     title = {Spectral properties of partial automorphisms of~a~binary rooted tree},
     journal = {Algebra and discrete mathematics},
     pages = {280--289},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a6/}
}
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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/