Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random walk approach to the analytic solution of random systems with
  multiplicative noise - the Anderson localization problem   We discuss here in detail a new analytical random walk approach to
calculating the phase-diagram for spatially extended systems with
multiplicative noise. We use the Anderson localization problem as an example.
The transition from delocalized to localized states is treated as a generalized
diffusion with a noise-induced first-order phase transition. The generalized
diffusion manifests itself in the divergence of averages of wavefunctions
(correlators). This divergence is controlled by the Lyapunov exponent $\gamma$,
which is the inverse of the localization length, $\xi=1/\gamma$. The appearance
of the generalized diffusion arises due to the instability of a fundamental
mode corresponding to correlators. The generalized diffusion can be described
in terms of signal theory, which operates with the concepts of input and output
signals and the filter function. Delocalized states correspond to bounded
output signals, and localized states to unbounded output signals, respectively.
The transition from bounded to unbounded signals is defined uniquely by the
filter function $H(z)$.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin