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
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
A Counterexample on Local Limits of Galton--Watson Trees
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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