Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time evolution of dense multigraph limits under edge-conservative
  preferential attachment dynamics   We define the edge reconnecting model, a random multigraph evolving in time.
At each time step we change one endpoint of a uniformly chosen edge: the new
endpoint is chosen by linear preferential attachment. We consider a sequence of
edge reconnecting models where the sequence of initial multigraphs is
convergent in a sense which is a natural generalization of the notion of
convergence of dense graph sequences, defined by Lovasz and Szegedy in
arXiv:math/0408173. We investigate how the limit object evolves under the edge
reconnecting dynamics if we rescale time properly: we give the complete
characterization of the time evolution of the limit object from its initial
state up to the stationary state, which is described in the companion paper
arXiv:1106.2058. In our proofs we use the theory of exchangeable arrays,
queuing and diffusion processes. The number of parallel edges and the degrees
evolve on different timescales and because of this the model exhibits subaging.

37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
7
The categories of this paper are: hep-th