CONTINUUM PERCOLATION FOR GAUSSIAN ZEROES AND GINIBRE EIGENVALUES

• 成果类型: Article
• 署名作者: Ghosh, Subhroshekhar; Krishnapur, Manjunath; Peres, Yuval
• 署名单位: Princeton University; Indian Institute of Science (IISC) - Bangalore; Microsoft
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1051
• 发表日期: 2016
• 页码: 3357-3384
• 关键词: random complex zeros; uniqueness; fluctuations

摘要

We study continuum percolation on certain negatively dependent point processes on R-2. Specifically, we study the Ginibre ensemble and the planar Gaussian zero process, which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion. For the Ginibre ensemble, we establish the uniqueness of infinite cluster in the supercritical phase. For the Gaussian zero process, we establish that a non-trivial critical radius exists, and we prove the uniqueness of infinite cluster in the supercritical regime.