Absolute continuity and singularity of Palm measures of the Ginibre point process

2014/06/16 by Hirofumi Osada, Osada, Hirofumi, Tomoyuki Shirai +1
Mathematics · Physics and Astronomy · #60B20 #60G55 #60K35 #82B21 #82C22 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.MP #math.PR #msc:60B20 #msc:60G55 #msc:60K35 #msc:82B21 #msc:82C22

paper · pdf · doi:10.48550/arxiv.1406.3913

47 pages, version (ii)

openalex publication_date 2014/06/16 · arxiv created 2015/04/05 · arxiv updated 2015/04/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove a dichotomy between absolute continuity and singularity of the Ginibre point process G and its reduced Palm measures \G_x, x ∈ ℂ^ℓ, ℓ = 0,1,2…\, namely, reduced Palm measures \G_x and \G_y for x ∈ ℂ^ℓ and y ∈ ℂⁿ are mutually absolutely continuous if and only if ℓ = n; they are singular each other if and only if ℓ \not= n. Furthermore, we give an explicit expression of the Radon-Nikodym density d\G_x/d \G_y for x, y ∈ ℂ^ℓ.

Citations

• Determinantal processes and completeness of random exponentials: the critical case

Related

• Palm measures and rigidity phenomena in point processes
• Determinantal point processes associated with Hilbert spaces of holomorphic functions
• Diffraction and Palm measure of point processes
• Equivalence of Palm measures for determinantal point processes governed by Bergman kernels
• Conditional measures of generalized Ginibre point processes