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

2017/03/27 by Alexander I. Bufetov, Bufetov, Alexander I., Shilei Fan +3 · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Random Matrices and Applications #Stochastic processes and statistical mechanics #math-ph #math.DS #math.FA #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1703.08978

31 pages

arxiv created 2017/03/27 · arxiv updated 2017/03/28

Abstract

For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A²(U, ω) over a domain U ⊂ ℂ^d, 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^∞(U)-module structure of A²(U, ω). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of U.

Citations

• Asymptotic expansion of polyanalytic Bergman kernels

Cited by

• Partial Bergman kernels and determinantal point processes on Kähler manifolds
• Kernels of conditional determinantal measures and the proof of the Lyons-Peres Conjecture

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