Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the limit distribution of Frobenius numbers   The Frobenius number g(a) of an integer vector a with positive coprime
coefficients is defined as the largest integer that does not have a
representation as a non-negative integer linear combination of the coefficients
of a. According to a recent result by Marklof, if a is taken to be random in an
expanding d-dimensional domain D, then g(a) (appropriately rescaled) has a
limit distribution. In the present paper we prove an asymptotic formula for the
(algebraic) tail behavior of this limit distribution. We also prove that the
corresponding upper bound on the probability of the Frobenius number being
large holds uniformly with respect to the expansion factor of the domain D.
Finally we prove that for large d, the limit distribution has almost all of its
mass concentrated in a fairly short interval. The techniques involved in the
proofs come from the geometry of numbers, and in particular we use results by
Schmidt on the distribution of sublattices of Z^m, and bounds by Rogers and
Schmidt on lattice coverings of space with convex bodies.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: nlin