Refined estimates for some basic random walks on the symmetric and alternating groups
Refined estimates for some basic random walks on the symmetric and alternating groups
复制标题
对对称组和交替组的一些基本随机游走的精确估计
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
J. Zúñiga
中科院分区：
文献类型：
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作者：
L. Saloff‐Coste;J. Zúñiga
我们给一些基本的随机游动的离散时间和连续时间版本的对称和交替群Sn和An的精细估计。我们考虑以下模型：随机转置，转置顶与随机，随机插入，和游动产生的一致措施的共轭类。在Sn和An上由共轭类上的一致测度生成的随机游动的情况下，我们证明了在连续时间中l2-截断有一个下界为（n/2）log n.这个结果，沿着Muller，Schlag-Puchta和Roichman的结果，证明了这些行走的连续时间版本可能比其离散时间对应物花费更长的时间来达到平稳性。
We give refined estimates for the discrete time and continuous time versions of some basic random walks on the symmetric and alternating groups Sn and An. We consider the following models: random transposition, transpose top with random, random insertion, and walks generated by the uniform measure on a conjugacy class. In the case of random walks on Sn and An generated by the uniform measure on a conjugacy class, we show that in continuous time the l 2 -cutoff has a lower bound of (n/2)log n. This result, along with the results of Muller, Schlage- Puchta and Roichman, demonstrates that the continuous time version of these walks may take much longer to reach stationarity than its discrete time counterpart.