Why an Immortal Branching Path Keeps Returning to the Minimum
A branching population seems to crowd its immortal lineage out of the minimum. A new theorem finds it returning, with reproduction setting the rhythm.
random walks
A Random Walk’s Endpoint Hides on a Measure-Zero Boundary
On a random hyperbolic tessellation, each walk’s endpoint law hides on a zero-measure set—even though averaging landscapes gives a uniform boundary.