276,333 research outputs found
Irreversible Aggregation and Network Renormalization
Irreversible aggregation is revisited in view of recent work on
renormalization of complex networks. Its scaling laws and phase transitions are
related to percolation transitions seen in the latter. We illustrate our points
by giving the complete solution for the probability to find any given state in
an aggregation process , given a fixed number of unit mass
particles in the initial state. Exactly the same probability distributions and
scaling are found in one dimensional systems (a trivial network) and well-mixed
solutions. This reveals that scaling laws found in renormalization of complex
networks do not prove that they are self-similar.Comment: 4 pages, 2 figure
Extended q-Gaussian and q-exponential distributions from Gamma random variables
The family of q-Gaussian and q-exponential probability densities fit the
statistical behavior of diverse complex self-similar non-equilibrium systems.
These distributions, independently of the underlying dynamics, can rigorously
be obtained by maximizing Tsallis "non-extensive" entropy under appropriate
constraints, as well as from superstatistical models. In this paper we provide
an alternative and complementary scheme for deriving these objects. We show
that q-Gaussian and q-exponential random variables can always be expressed as
function of two statistically independent Gamma random variables with the same
scale parameter. Their shape index determine the complexity q-parameter. This
result also allows to define an extended family of asymmetric q-Gaussian and
modified -exponential densities, which reduce to the previous ones when the
shape parameters are the same. Furthermore, we demonstrate that simple change
of variables always allow to relate any of these distributions with a Beta
stochastic variable. The extended distributions are applied in the statistical
description of different complex dynamics such as log-return signals in
financial markets and motion of point defects in fluid flows.Comment: 11 pages, 6 figure
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