Zeros of random tropical polynomials, random polygons and stick-breaking

2016 ◽  
Vol 368 (10) ◽  
pp. 7281-7303 ◽  
Author(s):  
Francois Baccelli ◽  
Ngoc Mai Tran
Keyword(s):  
Random Polygons

Generating equilateral random polygons in confinement III

2012 ◽  
Vol 45 (46) ◽  
pp. 465003 ◽  
Author(s):  
Y Diao ◽  
C Ernst ◽  
A Montemayor ◽  
U Ziegler
Keyword(s):  
Random Polygons

scholarly journals Random Polygons and Optimal Extrapolation Estimates of pi

2021 ◽  
Vol 9 (1) ◽  
pp. 241-249
Author(s):  
Shasha Wang ◽  
Wen-Qing Xu ◽  
Jitao Liu
Keyword(s):  
Unit Circle ◽  
Convergence Rates ◽  
Asymptotically Normal ◽  
Random Polygons

We construct optimal extrapolation estimates of π based on random polygons generated by n independent points uniformly distributed on a unit circle in R2. While the semiperimeters and areas of these random n-gons converge to π almost surely and are asymptotically normal as n → ∞, in this paper we develop various extrapolation processes to further accelerate such convergence. By simultaneously considering the random n-gons and suitably constructed random 2n-gons and then optimizing over functionals of the semiperimeters and areas of these random polygons, we derive several new estimates of π with faster convergence rates. These extrapolation improvements are also shown to be asymptotically normal as n → ∞.

Fractions of Particular Knots in Gaussian Random Polygons

1995 ◽  
Vol 64 (5) ◽  
pp. 1506-1518 ◽  
Author(s):  
Kyoichi Tsurusaki ◽  
Tetsuo Deguchi
Keyword(s):  
Random Polygons

Approximations to densities in geometric probability

1980 ◽  
Vol 17 (01) ◽  
pp. 145-153 ◽  
Author(s):  
H. Solomon ◽  
M. A. Stephens
Keyword(s):  
Monte Carlo ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Geometric Probability ◽  
Simple Approximation ◽  
Chi Square ◽  
Percentage Points ◽  
Random Polygons

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested, to approximate such densities; the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables (the area, the perimeter, and the number of sides) associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.

scholarly journals Average size of random polygons with fixed knot topology

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Hiroshi Matsuda ◽  
Akihisa Yao ◽  
Hiroshi Tsukahara ◽  
Tetsuo Deguchi ◽  
Ko Furuta ◽  
...  
Keyword(s):  
Random Polygons ◽  
Average Size

Generating equilateral random polygons in confinement

2011 ◽  
Vol 44 (40) ◽  
pp. 405202 ◽  
Author(s):  
Y Diao ◽  
C Ernst ◽  
A Montemayor ◽  
U Ziegler
Keyword(s):  
Random Polygons

scholarly journals Generating random polygons with given vertices

1996 ◽  
Vol 6 (5) ◽  
pp. 277-290 ◽  
Author(s):  
Chong Zhu ◽  
Gopalakrishnan Sundaram ◽  
Jack Snoeyink ◽  
Joseph S.B. Mitchell
Keyword(s):  
Random Polygons
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