Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing exchangeable pairs by diffusion on manifolds and its
  application   We construct a continuous family of exchangeable pairs by perturbing the
random variable through diffusion processes on manifold in order to apply Stein
method to certain geometric settings. We compare our perturbation by diffusion
method with other approaches of building exchangeable pairs and show that our
perturbation scheme cooperates with the infinitesimal version of Stein's method
harmoniously. More precisely, our exchangeable pairs satisfy a key condition in
the infinitesimal Stein's method in general. Based on the exchangeable pairs,
we are able to extend the approximate normality of eigenfunctions of Laplacian
on compact manifold to eigenfunctions of Witten Laplacian, which is of the
form:$\Delta_w = \Delta - \nabla H$. We then apply our abstract theorem to
recover a central limit result of linear statistics on sphere. Finally, we
prove an an infinitesimal version of Stein's method for exponential
distribution and combine it with our continuous family of exchangeable pairs to
extend an approximate exponentiality result of $|Tr U|^2$, where $Tr U$ is the
trace of the first power of a matrix $U$ sampled from the Haar measure of
unitary group, to arbitrary power and its analog for general circular ensemble.

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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
21
The categories of this paper are: adap-org
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The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg