J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence

Abstract : We study Palm measures of determinantal point processes with $J$-Hermitian correlation kernels. A point process $\mathbb{P}$ on the punctured real line $\mathbb{R}^* =\mathbb{R}_{+}\sqcup \mathbb{R}_{-}$ is said to be balanced rigid if for any precompact subset $B \subset\mathbb{R}^*$, the difference between the numbers of particles of a configuration inside $B \cap \mathbb{R}_{+}$ and $B \cap\mathbb{R}_{-}$ is almost surely determined by the configuration outside $B$. The point process $\mathbb{P}$ is said to have the balanced Palm equivalence property if any reduced Palm measure conditioned at $2n$ distinct points, $n$ in $\mathbb{R}_{+}$ and $n$ in $\mathbb{R}_{-}$ , is equivalent to $\mathbb{P}$. 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.
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Pré-publication, Document de travail
2017
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Dernière modification le : mercredi 12 décembre 2018 - 15:17:07
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  • HAL Id : hal-01483624, version 1

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Alexander I. Bufetov, Yanqi Qiu. J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence. 2017. 〈hal-01483624〉

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