Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fragmentation processes with an initial mass converging to infinity   We consider a family of fragmentation processes where the rate at which a
particle splits is proportional to a function of its mass. Let
$F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of
the masses present at time $t$ in a such process, starting from an initial mass
$m$. Let then $m\to \infty $. Under an assumption of regular variation type on
the dynamics of the fragmentation, we prove that the sequence
$(F\_{2}^{(m)},F\_{3}^{(m)},...)$ converges in distribution, with respect to
the Skorohod topology, to a fragmentation with immigration process. This holds
jointly with the convergence of $m-F\_{1}^{(m)}$ to a stable subordinator. A
continuum random tree counterpart of this result is also given: the continuum
random tree describing the genealogy of a self-similar fragmentation satisfying
the required assumption and starting from a mass converging to $\infty $ will
converge to a tree with a spine coding a fragmentation with immigration.

37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph