Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High excursion probabilities for Gaussian fields on smooth manifolds   Gaussian random fields on finite dimensional smooth manifolds whose variances
reach their maximum value at smooth submanifolds are considered. Exact
asymptotic behaviors of large excursion probabilities have been evaluated.
Vector Gaussian processes, chi-square processes, Bessel process, fractional
Bessel process, Bessel bridge are examples of application of this result.

32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci