{"id":"openai-math/Directional-transience-implies-ballisticity","pdf":"https://github.com/openai/math/blob/main/preprints/Directional-transience-implies-ballisticity-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Directional-transience-implies-ballisticity-September-23-2026","tags":["random-walks","probability","ballisticity"],"score":0,"title":"Directional transience implies ballisticity","domain":"Probability and statistical mechanics","family":"220","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that almost-sure transience in a fixed direction implies a deterministic limiting velocity with positive projection in that direction for nearest-neighbor random walks in independent and identically distributed uniformly elliptic environments on ℤ d , d ≥ 2. This resolves the ballisticity conjecture positively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Directional zero–one laws beyond iid environments and iid ballisticity"}