Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization fixed point of the KPZ universality class   The one dimensional Kardar-Parisi-Zhang universality class is believed to
describe many types of evolving interfaces which have the same characteristic
scaling exponents. These exponents lead to a natural renormalization/rescaling
on the space of such evolving interfaces. We introduce and describe the
renormalization fixed point of the Kardar-Parisi-Zhang universality class in
terms of a random nonlinear semigroup with stationary independent increments,
and via a variational formula. Furthermore, we compute a plausible formula the
exact transition probabilities using replica Bethe ansatz. The semigroup is
constructed from the Airy sheet, a four parameter space-time field which is the
Airy2 process in each of its two spatial coordinates. Minimizing paths through
this field describe the renormalization group fixed point of directed polymers
in a random potential. At present, the results we provide do not have
mathematically rigorous proofs, and they should at most be considered
proposals.

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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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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: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: adap-org