# [A Linear Clock for Random Walk on Tree-Weighted Planar Maps](linear-clock-random-walk-tree-weighted-planar-maps.pdf)

**Author:** OpenAI

**Date:** October 5, 2026

## Citation

```bibtex
@misc{OAI:A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026,
  author = {{OpenAI}},
  title = {{A Linear Clock for Random Walk on Tree-Weighted Planar Maps}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026/linear-clock-random-walk-tree-weighted-planar-maps.pdf}{OAI:A-Linear-Clock-for-Random-Walk-on-Tree-Weighted-Planar-Maps-October-5-2026}},
  year = {2026}
}
```