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In this paper we consider random walks on Galton-Watson trees with randomconductances. On these trees, the distance of the walker to the root satisfiesa law of large numbers with limit the effective velocity, or speed of the walk.We study the regularity of the speed as a function of the distribution ofconductances, in particular when the distribution of conductances converges toa non-elliptic limit.

The speed of random walk on Galton-Watson trees with vanishing conductances