Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local dimensions of random homogeneous self-similar measures: strong
  separation and finite type   We study the multifractal analysis of self-similar measures arising from
random homogeneous iterated function systems. Under the assumption of the
uniform strong separation condition, we see that this analysis parallels that
of the deterministic case. The overlapping case is more complicated; we
introduce the notion of finite type for random homogeneous iterated function
systems and give a formula for the local dimensions of finite type, regular,
random homogeneous self-similar measures in terms of Lyapunov exponents of
certain transition matrices. We show that almost all points with respect to
this measure are described by a distinguished subset called the essential
class, and that the dimension of the support can be computed almost surely from
knowledge of this essential class. For a special subcase, that we call
commuting, we prove that the set of attainable local dimensions is almost
surely a closed interval. Particular examples of such random measures are
analyzed in more detail.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom