# Random Walks and Brownian Motion Lecture 4

@inproceedings{Peled2011RandomWA, title={Random Walks and Brownian Motion Lecture 4}, author={R. Peled}, year={2011} }

This lecture deals primarily with recurrence for general random walks. We present several criteria for a random walk to be recurrent, and prove Polya's theorem on recurrence and transience for the simple random walk on Z d 1 Recurrence for general random walks Remember the following result from the previous lecture: Every 1-dimensional random walk S n satisfies exactly one of the following almost surely: (i) S n = 0 for every n. (iv) lim sup S n = ∞ and lim inf S n = −∞. We would like to… Expand

#### References

One-dimensional random walks. http://galton.uchicago.edu/ lalley/Courses

- One-dimensional random walks. http://galton.uchicago.edu/ lalley/Courses