Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete harmonic functions for non-symmetric Laplace operators in the
  quarter plane   We construct harmonic functions in the quarter plane for discrete Laplace
operators. In particular, the functions are conditioned to vanish on the
boundary and the Laplacians admit coefficients associated with transition
probabilities of non-symmetric random walks. By solving a boundary value
problem for generating functions of harmonic functions, we deduce explicit
expressions for the generating functions in terms of conformal mappings. These
mappings are yielded from a conformal welding problem with quasisymmetric shift
and contain information about the growth of harmonic functions. Further, we
describe the set of harmonic functions as a vector space isomorphic to the
space of formal power series.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th