%0 Journal Article
%T J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence
%+ Institut de Mathématiques de Marseille (I2M)
%+ Steklov Mathematical Institute [Moscow] (SMI | RAS)
%+ Institute for Information Transmission Problems
%+ Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow] (HSE)
%+ Institut de Mathématiques de Toulouse UMR5219 (IMT)
%A Bufetov, Alexander I.
%A Qiu, Yanqi
%< avec comité de lecture
%@ 0025-5831
%J Mathematische Annalen
%I Springer Verlag
%V 371
%N 1-2
%P 127-188
%8 2018
%D 2018
%R 10.1007/s00208-017-1627-y
%K Determinantal point processes
%K J-Hermitian kernel
%K Whittaker kernels
%K L-processes
%K Palm measures
%K balanced rigidity
%K balanced Palm equivalence property
%Z Mathematics [math]/Probability [math.PR]
%Z Mathematics [math]/Functional Analysis [math.FA]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01483624/document
%2 https://hal.science/hal-01483624/file/1512.07553.pdf
%L hal-01483624
%U https://hal.science/hal-01483624
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-AMU
%~ INSA-TOULOUSE
%~ EC-MARSEILLE
%~ IMT
%~ I2M
%~ I2M-2014-
%~ UT1-CAPITOLE
%~ CERCLE
%~ INSA-GROUPE
%~ AMIDEX
%~ TEST-HALCNRS
%~ ANR
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP