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

Abstract

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