5 papers · 1 filter
An FPRAS for Counting Common Bases of Two Matroids
Xiaoyu Chen, Kuikui Liu
We design the first polynomial-time algorithms for approximately counting and almost uniformly sampling common bases of two matroids given by their independence oracles. Moreover,…
Spectral Gap of Down-Up Walks via Trickle-Down: A Simplified and Sharpened Analysis
Xiaoyu Chen, Kuikui Liu
Local-to-global techniques for establishing spectral gaps have played a central role in the modern theory of Markov chain mixing times and the theory of high-dimensional expanders.…
A Spectral Local-to-Global Principle for Spin Systems on Graphs with Girth At Least Five
Xiaoyu Chen, Kuikui Liu
It is proved that, for every , the Glauber dynamics for the uniform distribution on proper -colorings is rapidly mixing when and the underlying graph…
Edge-Tilting Field Dynamics: Rapid Mixing at the Uniqueness Threshold and Optimal Mixing for Swendsen-Wang Dynamics
Xiaoyu Chen, Zhe Ju, Tianshun Miao +2
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of ant…
Subquadratic Counting via Perfect Marginal Sampling
Xiaoyu Chen, Zongchen Chen, Kuikui Liu +1
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde…