贺鑫. Galton--Watson~树的局部极限的一个反例[J]. 应用概率统计, 2018, 34(1): 1-7. DOI: 10.3969/j.issn.1001-4268.2018.01.001
引用本文: 贺鑫. Galton--Watson~树的局部极限的一个反例[J]. 应用概率统计, 2018, 34(1): 1-7. DOI: 10.3969/j.issn.1001-4268.2018.01.001
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HE Xin. A Counterexample on Local Limits of Galton--Watson Trees[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(1): 1-7. DOI: 10.3969/j.issn.1001-4268.2018.01.001
Citation: HE Xin. A Counterexample on Local Limits of Galton--Watson Trees[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(1): 1-7. DOI: 10.3969/j.issn.1001-4268.2018.01.001
shu

Galton--Watson~树的局部极限的一个反例

A Counterexample on Local Limits of Galton--Watson Trees

    摘要
  • 摘要: 本文考虑后代分布具有有界支撑的~Galton--Watson~树.我们证明在具有大的宽度这一条件概率分布下,Galton--Watson~树不会局部收敛到任何具有唯一一条无穷脊柱的随机树.

     

    Abstract: Take any subcritical offspring distribution with bounded support and consider the corresponding Galton--Watson tree. In this short note we condition this Galton--Watson tree on large width and show that the conditioned tree does not converge locally to any random tree with at most one infinite spine.

     

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