Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the longest common subsequence of independent random permutations
  invariant under conjugation   Bukh and Zhou conjectured that the expectation of the length of the longest
common subsequence of two i.i.d random permutations of size $n$ is greater than
$\sqrt{n}$. We prove in this paper that there exists a universal constant $n_1$
such that their conjecture is satisfied for any pair of i.i.d random
permutations of size greater than $n_1$ with distribution invariant under
conjugation.
  We prove also that asymptotically, this expectation is at least of order
$2\sqrt{n}$ which is the asymptotic behaviour of the uniform setting. More
generally, in the case where the laws of the two permutations are not
necessarily the same, we gibe a lower bound for the expectation. In particular,
we prove that if one of the permutations is invariant under conjugation and
with a good control of the expectation of the number of its cycles, the
limiting fluctuations of the length of the longest common subsequence are of
Tracy-Widom type. This result holds independently of the law of the second
permutation.

35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an