Efficient mixing of product walks on product groups
- Mathé, Peter
2010 Mathematics Subject Classification
- Product random walk, mixing time
We are going to study the mixing behavior of product-type random walks on product groups. This study is inspired by the investigation of the relaxation of random walks on d-dimensional grids with possibly direction dependent mesh size. Typically such walks are designed to randomly visit a coordinate direction and then to carry out a random step within the chosen component according to some random walk in this direction. We will derive a dependence of the mixing times of such random walks in terms of the component mixing times. If we are free to optimize the random visiting scheme, then we can speed up mixing in case the component mixing times vary much. In more homogeneous situations the overall mixing time is bounded by a multiple of the sum of the single ones times the logarithm of the number of components.