Geodesic
Limit spectral measures of matrix distributions of metric triples
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 106-110.

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

The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on $L^2(\mu)$ with kernel $\rho$. An example in which there is no deterministic spectral measure is constructed.
Keywords: metric triples, limit measures
Mots-clés : spectra, Cauchy distribution. 
@article{FAA_2023_57_2_a7,
     author = {A. M. Vershik and F. V. Petrov},
     title = {Limit spectral measures of matrix distributions of metric triples},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {106--110},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a7/}
}
TY  - JOUR
AU  - A. M. Vershik
AU  - F. V. Petrov
TI  - Limit spectral measures of matrix distributions of metric triples
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2023
SP  - 106
EP  - 110
VL  - 57
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a7/
LA  - ru
ID  - FAA_2023_57_2_a7
ER  - 
%0 Journal Article
%A A. M. Vershik
%A F. V. Petrov
%T Limit spectral measures of matrix distributions of metric triples
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2023
%P 106-110
%V 57
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a7/
%G ru
%F FAA_2023_57_2_a7
A. M. Vershik; F. V. Petrov. Limit spectral measures of matrix distributions of metric triples. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 2, pp. 106-110. http://geodesic.mathdoc.fr/item/FAA_2023_57_2_a7/

[1] V. Koltchinskii, E. Gine, Bernoulli, 6:1 (2000), 113–167 | DOI | MR | Zbl

[2] A. M. Vershik, UMN, 59:2(356) (2004), 65–104 | DOI | MR

[3] M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhauser, Boston, 1999 | MR | Zbl

[4] E. Bogomolny, O. Bohigas, C. Schmit, J. Phys. A, 36:12 (2003), 3595–3616 | DOI | MR | Zbl

[5] V. Bentkus, F. Gotze, Ann. Probab., 27:1 (1999), 454–521 | DOI | MR | Zbl

[6] G. Olshanski, A. Vershik, Contemporary Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 175, Amer. Math. Soc., Providence, RI, 1996, 137–175 | MR | Zbl

[7] D. Pickrell, Pacific J. Math., 150:1 (1991), 139–166 | DOI | MR | Zbl

[8] A. M. Vershik, F. V. Petrov, Europ. J. Math., 8:suppl. 2 (2022), 481–493 | DOI | MR | Zbl

[9] V. S. Korolyuk, Yu. V. Borovskikh, Teoriya $U$-statistik, Naukova dumka, Kiev, 1989 | MR

[10] I. A. Ibragimov, Yu. V. Linnik, Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965

[11] A. M. Vershik, P. B. Zatitskiy, F. V. Petrov, Cent. Europ. J. Math., 11:3 (2013), 379–400 | MR | Zbl

[12] A. M. Vershik, G. Veprev, P. B. Zatitskii, “Dinamika metrik v prostranstvakh s meroi i masshtabirovannaya entropiya”, UMN (to appear)