Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularly continuous spectrum of a self-similar Laplacian on the
  half-line   We investigate the spectrum of the self-similar Laplacian, which generates
the so-called "$pq$ random walk" on the integer half-line $\mathbb{Z}_+$. Using
the method of spectral decimation, we prove that the spectral type of the
Laplacian is singularly continuous whenever $p\neq \frac{1}{2}$. This serves as
a toy model for generating singularly continuous spectrum, which can be
generalized to more complicated settings. We hope it will provide more insight
into Fibonacci and other weakly self-similar models.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio