Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian
  case   We study the Kardar-Parisi-Zhang equation on the half-line $x \geq 0$ with
Neumann type boundary condition. Stationary measures of the KPZ dynamics were
characterized in recent work: they depend on two parameters, the boundary
parameter $u$ of the dynamics, and the drift $-v$ of the initial condition at
infinity. We consider the fluctuations of the height field when the initial
condition is given by one of these stationary processes. At large time $t$, it
is natural to rescale parameters as $(u,v)=t^{-1/3}(a,b)$ to study the critical
region. In the special case $a+b=0$, treated in previous works, the stationary
process is simply Brownian. However, these Brownian stationary measures are
particularly relevant in the bound phase ($a<0$) but not in the unbound phase.
For instance, starting from the flat or droplet initial data, the height field
near the boundary converges to the stationary process with $a>0$ and $b=0$,
which is not Brownian. For $a+b\geqslant 0$, we determine exactly the large
time distribution $F_{a,b}^{\rm stat}$ of the height function $h(0,t)$. As an
application, we obtain the exact covariance of the height field in a half-line
at two times $1\ll t_1\ll t_2$ starting from stationary initial data, as well
as estimates, when starting from droplet initial data, in the limit $t_1/t_2\to
1$.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: eess