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Non-universality for longest increasing subsequence of a random walk
- Publication Year :
- 2016
-
Abstract
- The longest increasing subsequence of a random walk with mean zero and finite variance is known to be $n^{1/2 + o(1)}$. We show that this is not universal for symmetric random walks. In particular, the symmetric Ultra-fat tailed random walk has a longest increasing subsequence that is asymptotically at least $n^{0.690}$ and at most $n^{0.815}$. An exponent strictly greater than $1/2$ is also shown for the symmetric stable-$\alpha$ distribution when $\alpha$ is sufficiently small.
- Subjects :
- Mathematics - Probability
60C05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1602.02207
- Document Type :
- Working Paper