Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition for extremes of a family of stationary multiple-stable
  processes   We investigate a family of multiple-stable processes that may exhibit either
long-range or short-range dependence, depending on the parameters. There are
two parameters for the processes, the memory parameter $\beta\in(0,1)$ and the
multiplicity parameter $p\in\mathbb N$. We investigate the macroscopic limit of
extremes of the process, in terms of convergence of random sup-measures, for
the full range of parameters. Our results show that (i) the extremes of the
process exhibit long-range dependence when $\beta_p := p\beta-p+1\in(0,1)$,
with a new family of random sup-measures arising in the limit, (ii) the
extremes are of short-range dependence when $\beta_p<0$, with independently
scattered random sup-measures arising in the limit, and (iii) there is a
delicate phase transition at the critical regime $\beta_p = 0$.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga