Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic random walks in Riemannian and sub-Riemannian geometry via
  volume sampling   We relate some basic constructions of stochastic analysis to differential
geometry, via random walk approximations. We consider walks on both Riemannian
and sub-Riemannian manifolds in which the steps consist of travel along either
geodesics or integral curves associated to orthonormal frames, and we give
particular attention to walks where the choice of step is influenced by a
volume on the manifold. A primary motivation is to explore how one can pass, in
the parabolic scaling limit, from geodesics, orthonormal frames, and/or volumes
to diffusions, and hence their infinitesimal generators, on sub-Riemannian
manifolds, which is interesting in light of the fact that there is no
completely canonical notion of sub-Laplacian on a general sub-Riemannian
manifold. However, even in the Riemannian case, this random walk approach
illuminates the geometric significance of Ito and Stratonovich stochastic
differential equations as well as the role played by the volume.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys