## Power-law statistics and universal scaling in the absence of
criticality.

#### Jonathan Touboul and Alain Destexhe

*Physical Review E* 95: 012413, 2017

## Abstract:

Critical states are sometimes identified experimentally through
power-law statistics or universal scaling functions. We show here
that such features naturally emerge from networks in self-sustained
irregular regimes away from criticality. In these regimes,
statistical physics theory of large interacting systems predict a
regime where the nodes have independent and identically distributed
dynamics. We thus investigated the statistics of a system in which
units are replaced by independent stochastic surrogates, and found
the same power-law statistics, indicating that these are not
sufficient to establish criticality. We rather suggest that these
are universal features of large-scale networks when considered
macroscopically. These results put caution on the interpretation of
scaling laws found in nature.

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