Rigidity of Determinantal Point Processes with the Airy, the Bessel and the Gamma Kernel

Abstract

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme of Ghosh [6], Ghosh and Peres [7]: the main step is the construction of a sequence of additive statistics with variance going to zero.

arXiv comment10 pages

References in corpus (5)

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• Determinantal Processes and Independence
• Level-Spacing Distributions and the Bessel Kernel
• Rigidity and Tolerance in Gaussian zeroes and Ginibre eigenvalues: quantitative estimates
• Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces

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