论文标题
对对称超脂肪随机步行的最长增加子序列的缩放行为的数值研究
A numerical investigation into the scaling behavior of the longest increasing subsequences of the symmetric ultra-fat tailed random walk
论文作者
论文摘要
一系列相关随机变量序列的最长增加的子序列（LIS）是一个基本数量，潜在的应用只有最近才开始受到适当的关注。在这里，我们调查了所谓的对称超脂肪随机步行的LIS长度的行为，该步行在数学文献中的抽象环境中以前引入。在明确构建超脂肪的随机步行后，我们从数值上发现，其lis的预期长度$ l_ {n} $缩放的长度像$ \ langle l_ {n} \ rangle \ sim n^n^0.716} $一样，确实表明了lis的行为。非常重的尾巴$α$稳定分布。我们还发现，$ l_ {n} $的分布似乎是普遍的，与其他重型尾巴随机步行所获得的结果一致。
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 $α$-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.
