Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random sampling of trivials words in finitely presented groups   We describe a novel algorithm for random sampling of freely reduced words
equal to the identity in a finitely presented group. The algorithm is based on
Metropolis Monte Carlo sampling. The algorithm samples from a stretched
Boltzmann distribution \begin{align*}\pi(w) &= (|w|+1)^{\alpha} \beta^{|w|}
\cdot Z^{-1} \end{align*} where $|w|$ is the length of a word $w$, $\alpha$ and
$\beta$ are parameters of the algorithm, and $Z$ is a normalising constant. It
follows that words of the same length are sampled with the same probability.
The distribution can be expressed in terms of the cogrowth series of the group,
which then allows us to relate statistical properties of words sampled by the
algorithm to the cogrowth of the group, and hence its amenability.
  We have implemented the algorithm and applied it to several group
presentations including the Baumslag-Solitar groups, some free products studied
by Kouksov, a finitely presented amenable group that is not subexponentially
amenable (based on the basilica group), and Richard Thompson's group $F$.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ