Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criticality and self-organization in branching processes: application to
  natural hazards   The statistics of natural catastrophes contains very counter-intuitive
results. Using earthquakes as a working example, we show that the energy
radiated by such events follows a power-law or Pareto distribution. This means,
in theory, that the expected value of the energy does not exist (is infinite),
and in practice, that the mean of a finite set of data in not representative of
the full population. Also, the distribution presents scale invariance, which
implies that it is not possible to define a characteristic scale for the
energy. A simple model to account for this peculiar statistics is a branching
process: the activation or slip of a fault segment can trigger other segments
to slip, with a certain probability, and so on. Although not recognized
initially by seismologists, this is a particular case of the stochastic process
studied by Galton and Watson one hundred years in advance, in order to model
the extinction of (prominent) families. Using the formalism of probability
generating functions we will be able to derive, in an accessible way, the main
properties of these models. Remarkably, a power-law distribution of energies is
only recovered in a very special case, when the branching process is at the
onset of attenuation and intensification, i.e., at criticality. In order to
account for this fact, we introduce the self-organized critical models, in
which, by means of some feedback mechanism, the critical state becomes an
attractor in the evolution of such systems. Analogies with statistical physics
are drawn. The bulk of the material presented here is self-contained, as only
elementary probability and mathematics are needed to start to read.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th