Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rescaled Levy-Loewner hulls and random growth   We consider radial Loewner evolution driven by unimodular L\'evy processes.
We rescale the hulls of the evolution by capacity, and prove that the weak
limit of the rescaled hulls exists. We then study a random growth model
obtained by driving the Loewner equation with a compound Poisson process. The
process involves two real parameters: the intensity of the underlying Poisson
process and a localization parameter of the Poisson kernel which determines the
jumps. A particular choice of parameters yields a growth process similar to the
Hastings-Levitov $\rm{HL}(0)$ model. We describe the asymptotic behavior of the
hulls with respect to the parameters, showing that growth tends to become
localized as the jump parameter increases. We obtain deterministic evolutions
in one limiting case, and Loewner evolution driven by a unimodular Cauchy
process in another. We show that the Hausdorff dimension of the limiting
rescaled hulls is equal to 1. Using a different type of compound Poisson
process, where the Poisson kernel is replaced by the heat kernel, as driving
function, we recover one case of the aforementioned model and
$\rm{SLE}(\kappa)$ as limits.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio