Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The correlated linking numbers of a Brownian loop with two arbitrary
  curves   The standard kinetic path integral for all spatially closed Brownian paths
(loops) of duration t weighted by the product mn is evaluated, where m and n
are the linking numbers of the Brownian loop with two arbitrary curves in 3D
space. The path integral thus indicates the extent to which these two linking
numbers are correlated, ranging from the value zero for far apart curves when
it is unlikely that the Brownian loop links with both, to (plus or minus)
infinity for nearly coincident curves. The result takes a form that loosely
resembles that for the mutual inductance of two current carrying curves in
magnetostatics, a double integral, but dependent on a single extra parameter,
the duration t of the path. The result for the equivalent two-dimensional
problem was given previously [Hannay 2018].

5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin