Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycle structure of the interchange process and representation theory   Consider the process of random transpositions on the complete graph. We use
representation theory to give an exact, simple formula for the expected number
of cycles of size k at time t, in terms of an incomplete Beta function. Using
this we show that the expected number of cycles of size k jumps from 0 to its
equilibrium value, 1/k, at the time where the giant component of the associated
random graph first exceeds k. Consequently we deduce a new and simple proof of
Schramm's theorem on random transpositions, that giant cycles emerge at the
same time as the giant component in the random graph. We also calculate the
"window" for this transition and find that it is quite thin. Finally, we give a
new proof of a result by the first author and Durrett that the random
transposition process exhibits a certain slowdown transition. The proof makes
use of a recent formula for the character decomposition of the number of cycles
of a given size in a permutation, and the Frobenius formula for the character
ratios.

27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat