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Non-backtracking random walks mix faster (2007)
| Content Provider | CiteSeerX |
|---|---|
| Author | Alon, Noga Benjamini, Itai Lubetzky, Eyal Sodin, Sasha |
| Description | We compute the mixing rate of a non-backtracking random walk on a regular expander. Using some properties of Chebyshev polynomials of the second kind, we show that this rate may be up to twice as fast as the mixing rate of the simple random walk. The closer the expander is to a Ramanujan graph, the higher the ratio between the above two mixing rates is. As an application, we show that if G is a high-girth regular expander on n vertices, then a typical non-backtracking random walk of length n on G does not visit a vertex more than log n (1 + o(1)) log log n times, and this result is tight. In this sense, the multi-set of visited vertices is analogous to the result of throwing n balls to n bins uniformly, in contrast to the simple random walk on G, which almost surely visits some vertex Ω(log n) times. 1 |
| File Format | |
| Language | English |
| Publisher Date | 2007-01-01 |
| Publisher Institution | Communications in Contemporary Mathematics, 9:585–603 |
| Access Restriction | Open |
| Subject Keyword | High-girth Regular Expander Regular Expander Simple Random Walk Typical Non-backtracking Random Walk Non-backtracking Random Walk Second Kind Chebyshev Polynomial Ramanujan Graph Visited Vertex Log Log Time |
| Content Type | Text |
| Resource Type | Article |
