Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: John's Walk   We present an affine-invariant random walk for drawing uniform random samples
from a convex body $\mathcal{K} \subset \mathbb{R}^n$ that uses maximum volume
inscribed ellipsoids, known as John's ellipsoids, for the proposal
distribution. Our algorithm makes steps using uniform sampling from the John's
ellipsoid of the symmetrization of $\mathcal{K}$ at the current point. We show
that from a warm start, the random walk mixes in $\widetilde{O}(n^7)$ steps
where the log factors depend only on constants associated with the warm start
and desired total variation distance to uniformity. We also prove polynomial
mixing bounds starting from any fixed point $x$ such that for any chord $pq$ of
$\mathcal{K}$ containing $x$, $\left|\log \frac{|p-x|}{|q-x|}\right|$ is
bounded above by a polynomial in $n$.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga