Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordered random walks   We construct the conditional version of $k$ independent and identically
distributed random walks on $\R$ given that they stay in strict order at all
times. This is a generalisation of so-called non-colliding or non-intersecting
random walks, the discrete variant of Dyson's Brownian motions, which have been
considered yet only for nearest-neighbor walks on the lattice. Our only
assumptions are moment conditions on the steps and the validity of the local
central limit theorem. The conditional process is constructed as a Doob
$h$-transform with some positive regular function $V$ that is strongly related
with the Vandermonde determinant and reduces to that function for simple random
walk. Furthermore, we prove an invariance principle, i.e., a functional limit
theorem towards Dyson's Brownian motions, the continuous analogue.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc