Lectures

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2011/03/03

14:45-15:45   Room #270 (Graduate School of Math. Sci. Bldg.)
Hirofumi Osada (Kyushu Univ.)
Singularity and absolute continuity of Palm measures of Ginibre random fields
(ENGLISH)
[ Abstract ]
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.