Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Schmidt and Summerer parametric geometry of numbers   Recently, W. M. Schmidt and L. Summerer introduced a new theory which allowed
them to recover the main known inequalities relating the usual exponents of
Diophantine approximation to a point in $\mathbb{R}^n$, and to discover new
ones. They first note that these exponents can be computed in terms of the
successive minima of a parametric family of convex bodies attached to the given
point. Then they prove that the $n$-tuple of these successive minima can in
turn be approximated up to bounded difference by a function from a certain
class. In this paper, we show that the same is true within a smaller and
simpler class of functions which we call rigid systems. We also show that
conversely, given a rigid system, there exists a point in $\mathbb{R}^n$ whose
associated family of convex bodies has successive minima which approximate that
rigid system up to bounded difference. As a consequence, the problem of
describing the joint spectrum of a family of exponents of Diophantine
approximation is reduced to combinatorial analysis.

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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin