Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance properties of random curves: an approach based on integral
  geometry   Traveled lengths statistic is a key quantity for characterizing stochastic
processes in bounded domains. For straight lines and diffusive random walks,
the average length of the trajectories through the domain is independent of the
random walk characteristics and depends only on the ratio of the volume domain
over its surface, a behavior that has been recently observed experimentally for
exponential jump processes. In this article, based solely on geometrical
concepts, we extend this remarkable property to any d-dimensional random curves
with arbitrary lengths (finite or infinite), therefore including all kind of
random walks as well as fibers processes. Integral geometry will be central in
establishing this universal property of random trajectories in bounded domains.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc