Mixing of the Exclusion Process with Small Bias
Mixing of the Exclusion Process with Small Bias
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混合排除过程和小偏差
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Y. Peres
中科院分区：
文献类型：
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作者：
D. A. Levin;Y. Peres
我们分析了有偏排斥过程在长度为n的路径上的混合行为，eta _n$$βn趋于0，因为$$n
八箭头infty $$n→∞。我们证明了链序列有一个预截断，并在无偏排斥过程和常偏过程之间插值。随着偏置的增加，混合时间经历两个相变：一个是当eta _n$$βn是1 / n阶的，另一个当$$eta _n$$βn的阶为$$log n/n$logn/n。
We analyze the mixing behavior of the biased exclusion process on a path of length n as the bias $$eta _n$$βn tends to 0 as $$n
ightarrow infty $$n→∞. We show that the sequence of chains has a pre-cutoff, and interpolates between the unbiased exclusion and the process with constant bias. As the bias increases, the mixing time undergoes two phase transitions: one when $$eta _n$$βn is of order 1 / n, and the other when $$eta _n$$βn is order $$log n/n$$logn/n.