Equivalence of Palm measures for determinantal point processes governed by Bergman kernels

• 成果类型: Article
• 署名作者: Bufetov, Alexander I.; Fan, Shilei; Qiu, Yanqi
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; 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; Central China Normal University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0803-z
• 发表日期: 2018
• 页码: 31-69
• 关键词: ergodic decomposition; fermion

摘要

For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A2(U,.) over a domain U. Cd, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the H 8 (U)-module structure of A2(U,.). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of U.