Rigidity of Determinantal Point Processes with the Airy, the Bessel and the Gamma Kernel
نویسندگان
چکیده
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.
منابع مشابه
The Arctic Circle Boundary and the Airy Process
We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond.
متن کامل0 O ct 2 00 1 ASYMPTOTIC REPRESENTATION THEORY AND RIEMANN – HILBERT PROBLEM
We show how the Riemann–Hilbert problem can be used to compute correlation kernels for determinantal point processes arising in different models of asymptotic combinatorics and representation theory. The Whittaker kernel and the discrete Bessel kernel are computed as examples.
متن کاملOn the Scaling Limits of Determinantal Point Processes with Kernels Induced by Sturm–Liouville Operators
By applying an idea of Borodin and Olshanski [J. Algebra 313 (2007), 40–60], we study various scaling limits of determinantal point processes with trace class projection kernels given by spectral projections of selfadjoint Sturm–Liouville operators. Instead of studying the convergence of the kernels as functions, the method directly addresses the strong convergence of the induced integral opera...
متن کاملFrom Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge...
متن کاملInfinite determinantal measures
Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal point process and a convergent, but not integrable, multiplicative functional. Theorem 2, the main result announced in this note, gives an ex...
متن کامل