Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes |
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| Authors: | Tomoyuki Shirai Yoichiro Takahashi |
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| Affiliation: | a Department of Computational Science, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan
b Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan |
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| Abstract: | We introduce certain classes of random point fields, including fermion and boson point processes, which are associated with Fredholm determinants of certain integral operators and study some of their basic properties: limit theorems, correlation functions, Palm measures etc. Also we propose a conjecture on an α-analogue of the determinant and permanent. |
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| Keywords: | Random field Point process Fredholm determinant Fermion process Boson process α-Determinant Palm measure |
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