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How long is the convex minorant of a one-dimensional random walk?

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 نشر من قبل Alexander Marynych
 تاريخ النشر 2019
  مجال البحث
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We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with different limit distributions for this length. Among other tools, a representation of the convex minorant of a random walk in terms of uniform random permutations is utilized.



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