Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volumetric Properties of the Convex Hull of an n-dimensional Brownian
  Motion   Let K be the convex hull of the path of a standard brownian motion B(t) in
R^n, taken at time 0 < t < 1. We derive formulas for the expected volume and
surface area of K. Moreover, we show that in order to approximate K by a
discrete version of K, namely by the convex hull of a random walk attained by
taking B(t_n) at discrete (random) times, the number of steps that one should
take in order for the volume of the difference to be relatively small is of
order n^3. Next, we show that the distribution of facets of K is in some sense
scale invariant: for any given family of simplices (satisfying some compactness
condition), one expects to find in this family a constant number of facets of
tK as t approaches infinity. Finally, we discuss some possible extensions of
our methods and suggest some further research.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph