Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large deviations for cascades of diffusions arising in oscillating
  systems of interacting Hawkes processes   We consider oscillatory systems of interacting Hawkes processes introduced in
Ditlevsen and Loecherbach (2017) to model multi-class systems of interacting
neurons together with the diffusion approximations of their intensity
processes. This diffusion, which incorporates the memory terms defining the
dynamics of the Hawkes process, is hypo-elliptic. It is given by a high
dimensional chain of differential equations driven by $2-$dimensional Brownian
motion. We study the large-population-, i.e., small noise-limit of its
invariant measure for which we establish a large deviation result in the spirit
of Freidlin and Wentzell.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex