Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-deviations/thermodynamic approach to percolation on the complete
  graph   We present a large-deviations/thermodynamic approach to the classic problem
of percolation on the complete graph. Specifically, we determine the
large-deviation rate function for the probability that the giant component
occupies a fixed fraction of the graph while all other components are
``small.'' One consequence is an immediate derivation of the ``cavity'' formula
for the fraction of vertices in the giant component. As a by-product of our
analysis we compute the large-deviation rate functions for the probability of
the event that the random graph is connected, the event that it contains no
cycles and the event that it contains only ``small'' components.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th