Mean perimeter and mean area of the convex hull over planar random walks
Mean perimeter and mean area of the convex hull over planar random walks
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平面随机游走上凸包的平均周长和平均面积
DOI：
10.1088/1742-5468/aa8c11
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Majumdar
中科院分区：
文献类型：
--
作者：
D. Grebenkov;Yann Lanoisel'ee;S. Majumdar
我们研究了具有对称连续跳跃分布的平面随机漫步n个连续位置上凸壳的几何性质。我们导出了平均周长的大n渐近性质。此外，我们计算了各向同性高斯跳变的特殊情况下的平均面积。虽然这些渐近的主要项是通用的，但次要（校正）项依赖于跳跃分布的更精细的细节，并描述了离散时间跳跃过程的“有限尺寸效应”，允许人们准确地计算平均周长和平均面积，即使对于小n，正如蒙特卡罗模拟所验证的那样。这对于处理离散时间跳跃过程的应用特别有价值，从微生物学中单粒子跟踪实验的统计分析到生态学中的家园范围估计。
We investigate the geometric properties of the convex hull over n successive positions of a planar random walk, with a symmetric continuous jump distribution. We derive the large n asymptotic behavior of the mean perimeter. In addition, we compute the mean area for the particular case of isotropic Gaussian jumps. While the leading terms of these asymptotics are universal, the subleading (correction) terms depend on the finer details of the jump distribution and describe a ‘finite size effect’ of discrete-time jump processes, allowing one to accurately compute the mean perimeter and the mean area even for small n, as verified by Monte Carlo simulations. This is particularly valuable for applications dealing with discrete-time jumps processes and ranging from the statistical analysis of single-particle tracking experiments in microbiology to home range estimations in ecology.
随机游走的凸包及其缩放限制
影响因子：
1.4
作者：
Wade A
通讯作者：
Wade A