Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Will Random Cone-wise Linear Systems Be Stable?   We consider a simple model for multidimensional cone-wise linear dynamics
around cusp-like equilibria. We assume that the local linear evolution is
either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with
$\mathbb{A}$, $\mathbb{B}$ independently drawn a rotationally invariant
ensemble of $N \times N$ matrices) depending on the sign of the first component
of $\mathbf{v}$. We establish strong connections with the random diffusion
persistence problem. When $N \to \infty$, we find that the Lyapounov exponent
is non self-averaging, i.e. one can observe apparent stability and apparent
instability for the same system, depending on time and initial conditions.
Finite $N$ effects are also discussed, and lead to cone trapping phenomena.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ