Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Off-diagonal decay of toric Bergman kernels   We study the off-diagonal decay of Bergman kernels $\Pi_{h^k}(z,w)$ and
Berezin kernels $P_{h^k}(z,w)$ for ample invariant line bundles over compact
toric projective \kahler manifolds of dimension $m$. When the metric is real
analytic, $P_{h^k}(z,w) \simeq k^m \exp - k D(z,w)$ where $D(z,w)$ is the
diastasis. When the metric is only $C^{\infty}$ this asymptotic cannot hold for
all $(z,w)$ since the diastasis is not even defined for all $(z,w)$ close to
the diagonal. We prove that for general $C^{\infty}$ metrics, $P_{h^k}(z,w)
\simeq k^m \exp - k D(z,w)$ as long as $w$ lies on the ${\mathbb R}_+^m$-orbit
of $z$, and for general $(z,w)$, $\limsup_{k \to \infty} \frac{1}{k} \log
P_{h^k}(z,w)
  \leq - D(z^*,w^*)$ where $D(z, w^*)$ is the diastasis between $z$ and the
translate of $w$ by $(S^1)^m$ to the ${\mathbb R}_+^m$ orbit of $z$,
complementary to Mike Christ's negative results (arXiv:1308.5644).

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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio