Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit shape of minimal difference partitions and fractional statistics   The class of minimal difference partitions MDP($q$) (with gap $q$) is defined
by the condition that successive parts in an integer partition differ from one
another by at least $q\ge 0$. In a recent series of papers by A. Comtet and
collaborators, the MDP($q$) ensemble with uniform measure was interpreted as a
combinatorial model for quantum systems with fractional statistics, that is,
interpolating between the classic Bose-Einstein ($q=0$) and Fermi-Dirac ($q=1$)
cases. This was done by formally allowing values $q \in (0,1)$ using an
analytic continuation of the limit shape of the corresponding Young diagrams
calculated for integer $q$. To justify this "replica-trick", we introduce a
more general model based on a variable MDP-type condition encoded by an integer
sequence $(q_i)$, whereby the (limiting) gap $q$ is naturally interpreted as
the Ces\`aro mean of $(q_i)$. In this model, we find the family of limit shapes
parameterized by $q \in [0,\infty)$ confirming the earlier answer, and also
obtain the asymptotics of the number of parts.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th