proofs or it didn't happen
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https://arxiv.org/abs/math/0001057 … A very very readable proof. But long though.
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I never worked out why that is... is there an easy proof?
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Knee-jerk instinct: you can fill a 2D plane with a single path of non-zero thickness (think of the game Snake, or spiraling from the center). That can't work in 3D.
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If anyone is interested, some times ago I wrote a simplified proof, along with other nice results related to random walkhttps://almogyalin.wordpress.com/2019/03/11/random-walk-riddles-compilation/ …
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Excelente. Gracias.
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What about dimensions in-between 2 and 3? Ie. fractals?
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These are the questions and answers that keep me coming back to Twitter.
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I am not sure if it refers to this, but the probability that a random walk will return to the origin is 1 for dimensions 1 and 2, in 3 dimensions the probability is aprox. equal 0.34... http://mathworld.wolfram.com/PolyasRandomWalkConstants.html …
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Yes. It can be shown to be equivalent to the case in question.
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