Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernels of conditional determinantal measures and the proof of the
  Lyons-Peres Conjecture   The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons
and Peres: for a determinantal point process governed by a reproducing kernel,
the system of kernels sampled at the particles of a random configuration is
complete in the range of the kernel. A key step in the proof, Lemma 1.11,
states that conditioning on the configuration in a subset preserves the
determinantal property, and the main Lemma 1.12 is a new local property for
kernels of conditional point processes. In Theorem 1.7 we prove the triviality
of the tail sigma-algebra for determinantal point processes governed by
self-adjoint kernels.

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The categories of this paper are: chem-ph
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph