Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A time-invariant random graph with splitting events   We introduce a process where a connected rooted multigraph evolves by
splitting events on its vertices, occurring randomly in continuous time. When a
vertex splits, its incoming edges are randomly assigned between its offspring
and a Poisson random number of edges are added between them. The process is
parametrised by a positive real $\lambda$ which governs the limiting average
degree. We show that for each value of $\lambda$ there is a unique random
connected rooted multigraph $M(\lambda)$ invariant under this evolution. As a
consequence, starting from any finite graph $G$ the process will almost surely
converge in distribution to $M(\lambda)$, which does not depend on $G$. We show
that this limit has finite expected size. The same process naturally extends to
one in which connectedness is not necessarily preserved, and we give a sharp
threshold for connectedness of this version.
  This is an asynchronous version, which is more realistic from the real-world
network point of view, of a process we studied in arXiv:1506.02697,
arXiv:1703.09011.

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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys