Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mean field model for the collective behaviour of interacting
  multi-species particles. Mathematical results and application to the inverse
  problem   The study of the normalized sum of random variables and its asymptotic
behaviour has been and continues to be a central chapter in probability and
statistical mechanics. When those variables are independent the central limit
theorem ensures that the sum with square-root normalization converges toward a
Gaussian distribution. The main topic of this thesis is the generalization of
the central limit theorem for spin random variable whose interaction is
described by a multi-species mean-field Hamiltonian. We found the conditions,
in terms of the interaction, that lead in the thermodynamic limit to a Gaussian
behaviour and those who lead to a higher order exponential distribution, under
the assumption that the Hamiltonian is a convex function of the magnetizations
and the first non vanishing partial derivatives of the pressure functional are
all the same order (homogeneity hypothesis). The thesis handle other two
problems concerning the multi-species mean-field model: the computation of the
exact solution of the thermodynamic limit of the pressure and the solution of
the inverse problem.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas