Abstract
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.
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B. Gerencsér is supported by NKFIH (National Research, Development and Innovation Office) Grant PD 121107. This work has been carried out during his stay at Université catholique de Louvain, Belgium. The work is supported by the DYSCO Network (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian Federal Science Policy Office, and by the Concerted Research Action (ARC) of the French Community of Belgium.
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Gerencsér, B., Hendrickx, J.M. Improved Mixing Rates of Directed Cycles by Added Connection. J Theor Probab 32, 684–701 (2019). https://doi.org/10.1007/s10959-018-0861-x
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DOI: https://doi.org/10.1007/s10959-018-0861-x