Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting fields of characteristic polynomials of random elements in
  arithmetic groups   We discuss rather systematically the principle, implicit in earlier works,
that for a "random" element in an arithmetic subgroup of a (split, say)
reductive algebraic group over a number field, the splitting field of the
characteristic polynomial, computed using any faitfhful representation, has
Galois group isomorphic to the Weyl group of the underlying algebraic group.
Besides tools such as the large sieve, which we had already used, we introduce
some probabilistic ideas (large deviation estimates for finite Markov chains)
and the general case involves a more precise understanding of the way Frobenius
conjugacy classes are computed for such splitting fields (which is related to a
map between regular elements of a finite group of Lie type and conjugacy
classes in the Weyl group which had been considered earlier by Carter and
Fulman for other purposes; we show in particular that the values of this map
are equidistributed).

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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: math-ph