QUASI-SYMMETRIES OF DETERMINANTAL POINT PROCESSES

• 成果类型: Article
• 署名作者: Bufetov, Alexander I.
• 署名单位: Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1198
• 发表日期: 2018
• 页码: 956-1003
• 关键词: level-spacing distributions; fermion; THEOREM

摘要

The main result of this paper is that determinantal point processes on R corresponding to projection operators with integrable kernels are quasiinvariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon-Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to the sine-process, as well as to determinantal point processes with the Bessel and the Airy kernels; Theorem 1.6 to the discrete sine-process and the Gamma kernel process. The paper answers a question of Grigori Olshanski.