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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - Eugenia Kochubinska
TI  - Spectral properties of partial automorphisms of~a~binary rooted tree
JO  - Algebra and discrete mathematics
PY  - 2018
SP  - 280
EP  - 289
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a6/
LA  - en
ID  - ADM_2018_26_2_a6
ER  - 
%0 Journal Article
%A Eugenia Kochubinska
%T Spectral properties of partial automorphisms of~a~binary rooted tree
%J Algebra and discrete mathematics
%D 2018
%P 280-289
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a6/
%G en
%F ADM_2018_26_2_a6
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