Probabilités
Diffraction et mesure de Palm des processus ponctuels

Présenté par : Jean-Pierre Kahane

Gouéré, Jean-Baptiste1
1 LaPCS, Université Claude Bernard Lyon I, bâtiment recherche [B], 50, avenue Tony-Garnier, Domaine de Gerland, 69366 Lyon cedex 07, France
Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 57-62.

En faisant appel à la notion de mesure de Palm, nous établissons l'existence de la mesure de diffraction pour tout processus ponctuel stationnaire et ergodique. Nous obtenons des caractérisations précises de ces mesures dans le cas de processus particuliers : sous-ensembles aléatoires de ℤ d , ensembles obtenus par la méthode « cut-and-project ».

Using the notion of Palm measure, we prove the existence of the diffraction measure of all stationary and ergodic point processes. We get precise expressions of those measures in the case of specific processes: stochastic subsets of ℤ d , sets obtained by the “cut-and-project” method.

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DOI : 10.1016/S1631-073X(02)00029-8
Gouéré, Jean-Baptiste 1

1 LaPCS, Université Claude Bernard Lyon I, bâtiment recherche [B], 50, avenue Tony-Garnier, Domaine de Gerland, 69366 Lyon cedex 07, France 
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Gouéré, Jean-Baptiste. Diffraction et mesure de Palm des processus ponctuels. Comptes Rendus. Mathématique, Tome 336 (2003) no. 1, pp. 57-62. doi : 10.1016/S1631-073X(02)00029-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)00029-8/

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