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You are watching: Random walk probability of returning to origin

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Downpack PDF Abstract: Associated to a random walk on $mathbbZ$ and also a positive integer $n$, thereis a return probcapability of the random walk returning to the origin after $n$procedures. An amazing question is once the collection of rerevolve probabilities uniquelydetermines the random walk. Tright here are trivial cases wbelow two differentrandom walks have the same rerotate probabilities. However, among random walks inwhich these instances perform not happen, our major outcome states that the returnprobabilities do identify the random walk. As a corollary, we will certainly acquire aresult dealing with the representation concept of $mathrmU(1)$.
Subjects: Probability (math.PR)
MSC classes: Primary 60J10, Secondary 22E45
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