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  "body": "\n## Summary\n\nA loop-erased random walk is the simple path obtained from a [[random walk|04VZE3FZXF]] by erasing its loops in the order in which they are created.\nIt is a random self-avoiding path, but its law differs from the uniform [[self-avoiding walk|E2BVEB570S]].\nThrough Wilson's algorithm it is the building block of the uniform [[spanning tree|0S4ZEZM7KE]] of a graph.\nIn the plane its scaling limit is the Schramm–Loewner evolution with parameter $2$.\n\n## Explanations\n\n### L1 human\n\nLet a random walker wander until it reaches a target, and record its path.\nEach time the walker comes back to a place it has already visited, cut out the loop it has just made.\nWhat remains is a path from start to target that never crosses itself.\nFor example, on the integer line the path $0, 1, 2, 1, 2, 3$ becomes $0, 1, 2, 3$ after the loop $2, 1, 2$ is erased.\n",
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