Let be the product of finite groups each having order and let be the probability measure which takes the value on each element of . In this paper we shall describe the point spectrum of in and the corresponding eigenspaces. In particular we shall see that the point spectrum occurs only for suitable choices of the numbers . We also compute the continuous spectrum of in in several cases. A family of irreducible representations of , parametrized on the continuous spectrum of , is here presented. Finally, we shall get a decomposition of the regular representation of by means of the Green function of and the decomposition is into irreducibles if and only if there are no true eigenspaces for .
Soit le produit libre de groupes finis d’ordre , et la probabilité prenant la valeur sur chaque élément de . Nous décrivons ici le spectre ponctuel de sur . On montre en particulier que ce spectre ponctuel apparaît pour certains choix des nombres , et les espaces propres correspondants dans sont décrits. Enfin, on obtient une décomposition de la représentation régulière de à l’aide de la fonction de Green de , cette décomposition étant irréductible si, et seulement si, n’a pas de sous-espace propre.
@article{AIF_1991__41_2_467_0, author = {Kuhn, M. Gabriella}, title = {Random walks on free products}, journal = {Annales de l'Institut Fourier}, pages = {467--491}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {41}, number = {2}, year = {1991}, doi = {10.5802/aif.1261}, zbl = {0725.60009}, mrnumber = {93a:43008}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1261/} }
TY - JOUR AU - Kuhn, M. Gabriella TI - Random walks on free products JO - Annales de l'Institut Fourier PY - 1991 SP - 467 EP - 491 VL - 41 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1261/ DO - 10.5802/aif.1261 LA - en ID - AIF_1991__41_2_467_0 ER -
Kuhn, M. Gabriella. Random walks on free products. Annales de l'Institut Fourier, Volume 41 (1991) no. 2, pp. 467-491. doi : 10.5802/aif.1261. https://aif.centre-mersenne.org/articles/10.5802/aif.1261/
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