  Introduced in its contemporary form by George Kingsley Zipf in 1946, but with
roots that go back to the work of Gaspard Monge in the 18th century, the
gravity law is the prevailing framework to predict population movement, cargo
shipping volume, inter-city phone calls, as well as bilateral trade flows
between nations. Despite its widespread use, it relies on adjustable parameters
that vary from region to region and suffers from known analytic
inconsistencies. Here we introduce a stochastic process capturing local
mobility decisions that helps us analytically derive commuting and mobility
fluxes that require as input only information on the population distribution.
The resulting radiation model predicts mobility patterns in good agreement with
mobility and transport patterns observed in a wide range of phenomena, from
long-term migration patterns to communication volume between different regions.
Given its parameter-free nature, the model can be applied in areas where we
lack previous mobility measurements, significantly improving the predictive
accuracy of most of phenomena affected by mobility and transport processes.
