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We prove that loop-erased random walks on finite pre-Sierpinski gaskets canbe extended to the infinite pre-Sierpinski gasket by virtue of the`erasing-larger-loops-first' method, and obtain the asymptotic behavior of thewalk as the number of steps increases, in particular, the displacement exponentand a law of the iterated logarithm.

Displacement exponent for loop-erased random walk on the Sierpi\'nski gasket