Phase Transition of the Reconstructability of a General Model with Different In-Community and Out-Community Mutations on an Infinite Tree
Phase Transition of the Reconstructability of a General Model with Different In-Community and Out-Community Mutations on an Infinite Tree
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无限树上具有不同群内和群外突变的一般模型可重构性的相变
DOI：
10.2139/ssrn.3461707
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Ning Ning
中科院分区：
文献类型：
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作者：
Wenjian Liu;Ning Ning
本文分析了树重构问题，即当<i>n→∞时，</i>树的<i>第n</i>层符号是否提供了根的信息，该问题在生物学、信息论和统计物理学等领域有着广泛的应用，并且它与随机块模型（SBM）下的聚类问题有着密切的联系.受最近提出的<i>q<sub>1</sub> +q<sub>2</sub></i>SBM的启发，我们扩展了Ising模型（Borgs et al. [2006]）和Potts模型（Sly [2011]）的经典工作，研究了一个通过不同的社区内和社区外转移概率融合Ising和Potts特征的一般模型，并严格建立了重建的精确条件.
In this paper, we analyze the tree reconstruction problem, which is to determine whether symbols at the <i>n</i>th level of the tree provide information on the root as <i>n→∞</i>.This problem has wide applications in various fields such as biology, information theory, and statistical physics, and its close connections to the clustering problem in the setting of the stochastic block model (SBM) have been well established. Inspired by the recently proposed <i>q<sub>1</sub>+q<sub>2</sub></i> SBM, we extend the classical works on the Ising model (Borgs et al. [2006]) and the Potts model (Sly [2011]), by studying a general model which incorporates the characteristics of both Ising and Potts through different in-community and out-community transition probabilities, and rigorously establishing the exact conditions for reconstruction.
DOI：
10.1214/15-aap1145
发表时间：
2013-09
期刊：
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影响因子：
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作者：
Elchanan Mossel;Joe Neeman;A. Sly
通讯作者：
Elchanan Mossel;Joe Neeman;A. Sly