Recurrence
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
A walk that always comes home, until it does not
Step left or right at random, forever, and the walk returns to where it started with certainty. On a grid it also returns. In space it does not, and about a third of walks leave and never come back.
The orbit that must come back
A system with finitely many states has to repeat itself. Poincaré showed the same thing holds when the states are a continuum — almost every starting point returns arbitrarily close to where it began, however complicated the rule, and the argument is the pigeonhole principle with volume in place of counting.
Named alongside it
The objects these essays reach for when they reach for this one.
Binomial distributionConvergenceDiffusionEntropyIndependenceIrrational rotationIterationLimitMeasureNormal distributionOrbitParity