Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shuffling cards by spatial motion   We propose a model of card shuffling where a pack of cards, spread as points
on a square table, are repeatedly gathered locally at random spots and then
spread towards a random direction. A shuffling of the cards is then obtained by
arranging the cards by their increasing $x$-coordinate values. When there are
$m$ cards on the table we show that this random ordering gets mixed in time
$O\left(\log m\right)$. Explicit constants are evaluated in a diffusion limit
when the position of $m$ cards evolves as an interesting $2m$-dimensional
non-reversible reflected jump diffusion in time. Our main technique involves
the use of multidimensional Skorokhod maps for double reflections in $[0,1]^2$
in taking the discrete to continuous limit. The limiting computations are then
based on the planar Brownian motion and properties of Bessel processes.

4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat