Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Excursion Probabilities of Isotropic and Locally Isotropic Gaussian
  Random Fields on Manifolds   Let $X= \{X(p), p\in M\}$ be a centered Gaussian random field, where $M$ is a
smooth Riemannian manifold. For a suitable compact subset $D\subset M$, we
obtain the approximations to excursion probability $\mathbb{P}\{\sup_{p\in D}
X(p) \ge u \}$, as $u\to \infty$, for two cases: (i) $X$ is smooth and
isotropic; (ii) $X$ is non-smooth and locally isotropic. For case (i), the
expected Euler characteristic approximation is formulated explicitly; while for
case (ii), it is shown that the asymptotics is similar to Pickands'
approximation on Euclidean space which involves Pickands' constant and the
volume of $D$. These extend the results in \citep{Cheng:2014} from sphere to
general Riemannian manifolds.

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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn