Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the loxodromic actions of Artin-Tits groups   Artin-Tits groups act on a certain delta-hyperbolic complex, called the
"additional length complex". For an element of the group, acting loxodromically
on this complex is a property analogous to the property of being pseudo-Anosov
for elements of mapping class groups. By analogy with a well-known conjecture
about mapping class groups, we conjecture that "most" elements of Artin-Tits
groups act loxodromically. More precisely, in the Cayley graph of a subgroup
$G$ of an Artin-Tits group, the proportion of loxodromically acting elements in
a ball of large radius should tend to one as the radius tends to infinity. In
this paper, we give a condition guaranteeing that this proportion stays away
from zero. This condition is satisfied e.g. for Artin-Tits groups of spherical
type, their pure subgroups and some of their commutator subgroups.

18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas