Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gibbs partitions: a comprehensive phase diagram   We study Gibbs partition models, also known as composition schemes. Our main
results comprehensively describe their phase diagram, including a phase
transition from the convergent case described in Stufler (2018, Random
Structures \& Algorithms) to a new dense regime characterized by a linear
number of components with fluctuations of smaller order quantified by an
$\alpha$-stable law for $1< \alpha \le 2$. We prove a functional scaling limit
for a process whose jumps correspond to the component sizes and discuss
applications to extremal component sizes. At the transition we observe a
mixture of the two asymptotic shapes. We also treat extended composition
schemes and prove a local limit theorem in an dilute regime with the limiting
law being related to an $\alpha$-stable law for $0< \alpha < 1$.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph