Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Temporal increments of the KPZ equation with general initial data   We consider the Cole-Hopf solution of the (1+1)-dimensional KPZ equation
$\mathcal{H}^f(t,x)$ started with initial data $f$. In this article, we study
the sample path properties of the KPZ temporal process $\mathcal{H}_t^f :=
\mathcal{H}^f(t,0)$. We show that for a very large class of initial data which
includes any deterministic continuous initial data that grows slower than
parabola ($f(x) \ll 1 + x^2$) as well as narrow wedge and stationary initial
data, temporal increments of $\mathcal{H}_t^f$ are well approximated by
increments of a fractional Brownian motion of Hurst parameter $\frac14$. As a
consequence, we obtain several sample path properties of KPZ temporal
properties including variation of the temporal process, law of iterated
logarithms, modulus of continuity and Hausdorff dimensions of the set of points
with exceptionally large increments.

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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio