Revisiting random polygonal lines iteratively generated on the plane. Issue 4 (25th April 2019)

• Record Type: Journal Article
• Authors: Santos, Rui; Martins, João Paulo; Felgueiras, Miguel; Ferreira, Susana
• Is Part Of: Computational and mathematical methods. Volume 1:Issue 4(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-04-25
• Subjects: bounding box -- convex hull -- nondegenerate asymptotic laws -- plane random curves -- renormalization -- simulation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1036
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract : Random polygonal lines iteratively generated on the plane can be drawn starting with a finite segment which is iteratively folded up, ie, all the segments of the open polygonal line are randomly folded up in each iteration. Moreover, a scale up factor must be used in this iterative procedure to ensure that the distance between the two endpoints of the generated random polygonal line converges to a nondegenerate random variable with finite mean. Hence, under adequate scale factor renormalization, some properties of these random polygonal lines are investigated by simulation, such as the square of the distance between the two endpoints, the diameter, the (minimum) bounding box, and the convex hull.