Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geodesics in first-passage percolation cross any pattern   In first-passage percolation, one places nonnegative i.i.d. random variables
(T (e)) on the edges of Z d. A geodesic is an optimal path for the passage
times T (e). Consider a local property of the time environment. We call it a
pattern. We investigate the number of times a geodesic crosses a translate of
this pattern. Under mild conditions, we show that, apart from an event with
exponentially small probability, this number is linear in the distance between
the extremities of the geodesic.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph