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.
The project was supported by the National Natural Science Foundation of China (Grant Nos. 11401012; 11671145) and the Natural Science Foundation of Shanghai (Grant No. 16ZR1409700).
Corresponding Authors:
HE Xin
E-mail: xinhe_math@163.com
