A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk · arXivDesk
2006.00366May 30, 2020A brief report on the LIS of ultra-fat tailed random walks, the construction of which may be of independent interest. Accepted for publication in Physics Letters A (2020)
A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk
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 Ln of its LIS scales with the length n of the walk like ⟨Ln⟩∼n0.716
Nearby in the stack
, 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
α
-stable distribution. We also found that the distribution of
Ln
seems to be universal, in agreement with results obtained for other heavy tailed random walks.