Improved Mixing Rates of Directed Cycles by Added Connection
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We investigate the mixing rate of a Markov chain where a combination of long distance edges and non-reversibility is introduced. As a first step, we focus here on the following graphs: starting from the cycle graph, we select random nodes and add all edges connecting them. We prove a square-factor improvement of the mixing rate compared to the reversible version of the Markov chain.
KeywordsMixing rate Random graphs Non-reversibility
Mathematics Subject Classification (2010)60J10 05C80
- 1.Addario-Berry, L., Lei, T.: The mixing time of the Newman–Watts small world. In: Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 18 Jan 2012, pp. 1661–1668 (2012)Google Scholar
- 6.Gerencsér, B.: Mixing times of Markov chains on a cycle with additional long range connections. arXiv:1401.1692 (2014)
- 7.Jerrum, M.: Mathematical foundations of the Markov chain Monte Carlo method. In: Habib, M., McDiarmid, C., Ramirez-Alfonsin, J., Reed, B. (eds.) Probabilistic Methods for Algorithmic Discrete Mathematics, vol. 16 of Algorithms and Combinatorics, pp. 116–165. Springer, Berlin (1998)CrossRefGoogle Scholar