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Non-universality for longest increasing subsequence of a random walk

Authors :
Pemantle, Robin
Peres, Yuval
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

Subjects :
Mathematics - Probability
60C05

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1602.02207
Document Type :
Working Paper