Abstract
In this paper we study the random walk on the hypercube (ℤ / 2ℤ)n which at each step flips k randomly chosen coordinates. We prove that the mixing time for this walk is of the order (n / k)logn. We also prove that if k = o(n) then the walk exhibits cutoff at (n / 2k)logn with window n / 2k.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1288-1299 |
| Number of pages | 12 |
| Journal | Advances in Applied Probability |
| Volume | 49 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 2017 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics
Keywords
- Ehrenfest urn model
- Hypercube
- coupling
- random walk