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In this chapter we discuss the loop-erased or Laplacian self-avoiding random walk. We will primarily use the loop-erased characterization of the walk because it is the one that allows for rigorous analysis of the model. In Proposition 7.3.1 we show that this is the same as the Laplacian random walk defined in Section 6.5.
KeywordsBrownian Motion Random Walk Indicator Function Standard Brownian Motion Logarithmic Correction
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