Abstract. Inthisnoteweprovethatafinitefamily{X1,...,Xd}ofrealr.v.’s that is exchangeable and such that (X1, . . . , Xd) is invariant with respect to a subgroup of SO(d) acting irreducibly, is actually invariant with respect to the action of the full group SO(d). Three immediate consequences are deduced: a characterization of isotropic spherical random eigenfunctions whose Fourier coefficients are exchangeable, an extension of Bernstein’s characterization of the Gaussian and a characterization of the Lebesgue measure on the share.
Baldi, P., Marinucci, D., Trapani, S. (2025). Exchangeability and irreducible rotational invariance. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. SERIES B, 153(2), 513-521 [10.1090/proc/17058].
Exchangeability and irreducible rotational invariance
Baldi, P;Marinucci, D;
2025-01-01
Abstract
Abstract. Inthisnoteweprovethatafinitefamily{X1,...,Xd}ofrealr.v.’s that is exchangeable and such that (X1, . . . , Xd) is invariant with respect to a subgroup of SO(d) acting irreducibly, is actually invariant with respect to the action of the full group SO(d). Three immediate consequences are deduced: a characterization of isotropic spherical random eigenfunctions whose Fourier coefficients are exchangeable, an extension of Bernstein’s characterization of the Gaussian and a characterization of the Lebesgue measure on the share.| File | Dimensione | Formato | |
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