Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On metric Ramsey-type phenomena   The main question studied in this article may be viewed as a nonlinear
analogue of Dvoretzky's theorem in Banach space theory or as part of Ramsey
theory in combinatorics. Given a finite metric space on n points, we seek its
subspace of largest cardinality which can be embedded with a given distortion
in Hilbert space. We provide nearly tight upper and lower bounds on the
cardinality of this subspace in terms of n and the desired distortion. Our main
theorem states that for any epsilon>0, every n point metric space contains a
subset of size at least n^{1-\epsilon} which is embeddable in Hilbert space
with O(\frac{\log(1/\epsilon)}{\epsilon}) distortion. The bound on the
distortion is tight up to the log(1/\epsilon) factor. We further include a
comprehensive study of various other aspects of this problem.

6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
29
The categories of this paper are: funct-an