Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive random walks and an identity for half-space SPDEs   The purpose of this article is threefold. First, we introduce a new type of
boundary condition for the multiplicative-noise stochastic heat equation on the
half space. This is essentially a Dirichlet boundary condition but with a
nontrivial normalization near the boundary which leads to inhomogeneous
transition densities (roughly, those of a Brownian \textit{meander}) within the
associated chaos series. Secondly, we prove a new convergence result of the
directed-polymer partition function in an octant to the multiplicative
stochastic heat equation with this type of boundary condition, which in turn
involves a detailed analysis of the aforementioned inhomogeneous Markov
process. Thirdly, as a corollary, we prove a surprising
equality-in-distribution for multiplicative-noise stochastic heat equations on
the half space with \textit{different} boundary conditions. This identity may
be seen as a precursor for proving Gaussian fluctuation behavior of
supercritical half-space KPZ at the origin.

18
The categories of this paper are: econ
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc