We study biased random walk on subcritical and supercritical Galton–Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which, in this case, always yield sub-ballisticity. This is contrary to the walk on the supercritical tree which always has some ballistic phase.

中文翻译：

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Galton-Watson 树上有偏随机游走的逃逸机制

我们研究了亚临界和超临界 Galton-Watson 树上的有偏随机游走，这些树有条件在瞬态亚弹道状态下生存。通过考虑具有无限方差的后代定律，我们扩展了先前已知的超临界树游动结果，并观察了亚临界树游动的新诱捕现象，在这种情况下，总是产生亚弹道性。这与总是具有一些弹道相的超临界树上的行走相反。