Improved Mixing Rates of Directed Cycles with Additional Sparse Interconnections

Balázs Gerencsér; Julien M. Hendrickx

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arXiv · 2307.09949

Improved Mixing Rates of Directed Cycles with Additional Sparse Interconnections

Balázs Gerencsér·Julien M. Hendrickx

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Abstract

We analyze the absolute spectral gap of Markov chains on graphs obtained from a cycle of $n$ vertices and perturbed only at approximately $n^{1/ρ}$ random locations with an appropriate, possibly sparse, interconnection structure. Together with a strong asymmetry along the cycle, the gap of the resulting chain can be bounded inversely proportionally by the longest arc length (up to logarithmic factors) with high probability, providing a significant mixing speedup compared to the reversible version.

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BibTeX RIS

Balázs Gerencsér, Julien M. Hendrickx. 2023-07-19. Improved Mixing Rates of Directed Cycles with Additional Sparse Interconnections. https://arxiv.org/abs/2307.09949

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