本文印刷
全画面プリント
講演会
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
2011年03月03日(木)
14:45-15:45 数理科学研究科棟(駒場) 270号室
長田 博文 氏 (九大数理)
Singularity and absolute continuity of Palm measures of Ginibre random fields
(ENGLISH)
長田 博文 氏 (九大数理)
Singularity and absolute continuity of Palm measures of Ginibre random fields
(ENGLISH)
[ 講演概要 ]
The Ginibre random point field is a probability measure on the configuration space over the complex plane $\\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\\beta = 2 $. This fact is justified by the integration by parts formula.
Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \\in \\mathbb{C}$ are mutually absolutely continuous.
The Ginibre random point field is a probability measure on the configuration space over the complex plane $\\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\\beta = 2 $. This fact is justified by the integration by parts formula.
Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \\in \\mathbb{C}$ are mutually absolutely continuous.
