Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrum of large random Markov chains: heavy-tailed weights on the
  oriented complete graph   We consider the random Markov matrix obtained by assigning i.i.d.
non-negative weights to each edge of the complete oriented graph. In this
study, the weights have unbounded first moment and belong to the domain of
attraction of an alpha-stable law. We prove that as the dimension tends to
infinity, the empirical measure of the singular values tends to a probability
measure which depends only on alpha, characterized as the expected value of the
spectral measure at the root of a weighted random tree. The latter is a
generalized two-stage version of the Poisson weighted infinite tree (PWIT)
introduced by David Aldous. Under an additional smoothness assumption, we show
that the empirical measure of the eigenvalues tends to a non-degenerate
isotropic probability measure depending only on alpha and supported on the unit
disc of the complex plane. We conjecture that the limiting support is actually
formed by a strictly smaller disc.

14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int