Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-similar behavior of the exchange-driven growth model with product
  kernel   We study the self-similar behavior of the exchange-driven growth model, which
describes a process in which pairs of clusters, consisting of an integer number
of monomers, interact through the exchange of a single monomer. The rate of
exchange is given by an interaction kernel $K(k,l)$ which depends on the sizes
$k$ and $l$ of the two interacting clusters and is assumed to be of product
form $(k\,l)^\lambda$ for $\lambda \in [0,2)$. We rigorously establish the
coarsening rates and convergence to the self-similar profile found by Ben-Naim
and Krapivsky [7]. For the explicit kernel, the evolution is linked to a
discrete weighted heat equation on the positive integers by a nonlinear
time-change. For this equation, we establish a new weighted Nash inequality
that yields scaling-invariant decay and continuity estimates. Together with a
replacement identity that links the discrete operator to its continuous analog,
we derive a discrete-to-continuum scaling limit for the weighted heat equation.
Reverting the time-change under the use of additional moment estimates, the
analysis of the linear equation yields coarsening rates and self-similar
convergence of the exchange-driven growth model.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg