Non-universality for longest increasing subsequence of a random walk
نویسندگان
چکیده
The longest increasing subsequence of a random walk with mean zero and finite variance is known to be n1/2+o(1). We show that this is not universal for symmetric random walks. In particular, the symmetric fat-tailed random walk has a longest increasing subsequence that is asymptotically at least n0.690 and at most n0.815. An exponent strictly greater than 1/2 is also shown for the symmetric stable-α distribution when α is sufficiently small.
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