Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability of graphs with large spectral gap by multicanonical Monte
  Carlo   Graphs with large spectral gap are important in various fields such as
biology, sociology and computer science. In designing such graphs, an important
question is how the probability of graphs with large spectral gap behaves. A
method based on multicanonical Monte Carlo is introduced to quantify the
behavior of this probability, which enables us to calculate extreme tails of
the distribution. The proposed method is successfully applied to random
3-regular graphs and large deviation probability is estimated.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex