Prove VelocityHemisphere (openai/math family 220: Directional zero–one laws and ballisticity in random…
Prove VelocityHemisphere (openai/math family 220: Directional zero–one laws and ballisticity in random…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 220 of the release, Directional zero–one laws and ballisticity in random environments…
The task
Context: this statement belongs to family 220 of the release, *Directional zero–one laws and ballisticity in random environments* (Probability and statistical mechanics). The family as a whole: On $\mathbb Z^d$, $d\ge3$, directional escape has probability zero or one for iid strictly elliptic nearest-neighbor…
Part of raising-heart/openai-math.