Invariant random fields in vector bundles and application to cosmology
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 4, p. 1068-1095

We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group G is obtained. We discuss an application to the theory of relic radiation, where G = SO(3). A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.

Nous développons la théorie des champs aléatoires invariants dans les fibrés vectoriels. Nous obtenons la décomposition spectrale d'un champ aléatoire invariant dans un fibré vectoriel homogène engendré par une représentation induite par un groupe de Lie compact et connexe. Nous discutons une application à la théorie du rayonnement fossile, où G = SO(3). Un théorème sur l'équivalence de deux groupes d'hypothèses cosmologiques est aussi démontré.

DOI : https://doi.org/10.1214/10-AIHP409
Classification:  60G60
Keywords: invariant random field, vector bundle, cosmic microwave background
@article{AIHPB_2011__47_4_1068_0,
     author = {Malyarenko, Anatoliy},
     title = {Invariant random fields in vector bundles and application to cosmology},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {4},
     year = {2011},
     pages = {1068-1095},
     doi = {10.1214/10-AIHP409},
     zbl = {1268.60072},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_4_1068_0}
}
Malyarenko, Anatoliy. Invariant random fields in vector bundles and application to cosmology. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 4, pp. 1068-1095. doi : 10.1214/10-AIHP409. http://www.numdam.org/item/AIHPB_2011__47_4_1068_0/

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