Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interacting diffusions on sparse graphs: hydrodynamics from local weak
  limits   We prove limit theorems for systems of interacting diffusions on sparse
graphs. For example, we deduce a hydrodynamic limit and the propagation of
chaos property for the stochastic Kuramoto model with interactions determined
by Erd\H{o}s-R\'{e}nyi graphs with constant mean degree. The limiting object is
related to a potentially infinite system of SDEs defined over a Galton-Watson
tree. Our theorems apply more generally, when the sequence of graphs
("decorated" with edge and vertex parameters) converges in the local weak
sense. Our main technical result is a locality estimate bounding the influence
of far-away diffusions on one another. We also numerically explore the
emergence of synchronization phenomena on Galton-Watson random trees, observing
rich phase transitions from synchronized to desynchronized activity among nodes
at different distances from the root.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg