Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level Lines of Gaussian Free Field I: Zero-Boundary GFF   Let $h$ be an instance of Gaussian Free Field in a planar domain. We study
level lines of $h$ starting from boundary points. We show that the level lines
are random continuous curves which are variants of SLE$_4$ path. We show that
the level lines with different heights satisfy the same monotonicity behavior
as the level lines of smooth functions. We prove that the time-reversal of the
level line coincides with the level line of $-h$. This implies that the
time-reversal of SLE$_4(\underline{\rho})$ process is still an
SLE$_4(\underline{\rho})$ process. We prove that the level lines satisfy
"target-independent" property. We also discuss the relation between Gaussian
Free Field and CLE$_4$.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys