Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of Majority Rule on Hypergraphs   A broad range of dynamical systems involve multi-body interactions, or group
interactions, which may not be encoded in traditional graphical structures. In
this work, we focus on a canonical example from opinion dynamics, the Majority
Rule, and investigate the possibility to represent and analyse the system by
means of hypergraphs. We explore the formation of consensus and restrict our
attention to interaction groups of size $3$, in order to simplify our analysis
from a combinatorial perspective. We propose different types of hypergraph
models, incorporating modular structure or degree heterogeneity, and recast the
dynamics in terms of Fokker-Planck equations, which allows us to predict the
transient dynamics toward consensus. Numerical simulations show a very good
agreement between the stochastic dynamics and theoretical predictions for large
population sizes.

24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th