Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of exclusion processes and KPZ equation to the KPZ fixed
  point   We show that under the 1:2:3 scaling, critically probing large space and
time, the height function of finite range asymmetric exclusion processes and
the KPZ equation converge to the KPZ fixed point, constructed earlier as a
limit of the totally asymmetric simple exclusion process through exact
formulas. Consequently, based on recent results of \cite{wu},\cite{DM20}, the
KPZ line ensemble converges to the Airy line ensemble. For the KPZ equation we
are able to start from a continuous function plus a finite collection of narrow
wedges. For nearest neighbour exclusions, we can take (discretizations) of
continuous functions with $|h(x)|\le C(1+\sqrt{|x|})$ for some $C>0$, or one
narrow wedge. For non-nearest neighbour exclusions, we are restricted at the
present time to a class of (random) initial data, dense in continuous functions
in the topology of uniform convergence on compacts. The method is by comparison
of the transition probabilities of finite range exclusion processes and the
totally asymmetric simple exclusion processes using energy estimates. Just
before posting the first version of this article, we learned that,
\emph{independently and at the same time and place}, B\'alint Vir\'ag found a
completely different proof of the convergence of the KPZ equation to the KPZ
fixed point. The methods invite extensions in different directions and it will
be very interesting to see how this plays out.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex