  The longest increasing subsequence (LIS) of a sequence of correlated random
variables is a basic quantity with potential applications that has started to
receive proper attention only recently. Here we investigate the behavior of the
length of the LIS of the so-called symmetric ultra-fat tailed random walk,
introduced earlier in an abstract setting in the mathematical literature. After
explicit constructing the ultra-fat tailed random walk, we found numerically
that the expected length $L_{n}$ of its LIS scales with the length $n$ of the
walk like $\langle L_{n} \rangle \sim n^{0.716}$, indicating that, indeed, as
far as the behavior of the LIS is concerned the ultra-fat tailed distribution
can be thought of as equivalent to a very heavy tailed $\alpha$-stable
distribution. We also found that the distribution of $L_{n}$ seems to be
universal, in agreement with results obtained for other heavy tailed random
walks.
