|J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence |
Auteur(s): Bufetov A., Qiu Yanqi
(Document sans référence bibliographique)
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We study Palm measures of determinantal point processes with J-Hermitian correlation kernels. A point process P on the punctured real line R * = R + ⊔ R − is said to be balanced rigid if for any precompact subset B ⊂ R * , the difference between the numbers of particles of a configuration inside B ∩ R + and B ∩ R − is almost surely determined by the configuration outside B. The point process P is said to have the balanced Palm equivalence property if any reduced Palm measure conditioned at 2n distinct points, n in R + and n in R − , is equivalent to the P. We formulate general criteria for determinantal point processes with J-Hermitian correlation kernels to be balanced rigid and to have the balanced Palm equivalence property and prove, in particular, that the determinantal point processes with Whit-taker kernels of Borodin and Olshanski are balanced rigid and have the balanced Palm equivalence property.