Complex systems and emergence

Emergent heavy-tailed distributions from a Markovian random walk

A small new random-walk paper has a big complex-systems lesson: heavy tails do not always need global memory, hidden shocks, or exotic jumps.

Emergent heavy-tailed distributions from a Markovian random walk
Visual brief for “Emergent heavy-tailed distributions from a Markovian random walk”.

What happened

Henrique S. Lima and Evaldo M. F. Curado describe a strictly local, discrete-time Markovian mechanism where the walker's step length depends on position. That local feedback is enough to produce a robust non-Gaussian stationary state with power-law tails over six decades.

This is why complex systems keep surprising us. Scale-free behavior can emerge from tiny rule changes when the rule changes the path the system is likely to take next. The macro pattern looks mysterious until the micro feedback loop is made explicit.

The builder's version: before blaming the whole network, look for the local feedback rule that quietly turns ordinary motion into extreme outcomes.

Source

Reported by Emergent heavy-tailed distributions from a Markovian random walk via arxiv.org, published May 21, 2026.