TY - JOUR
AU - Skliros, Aris
AU - Park, Wooram
AU - Chirikjian, Gregory S.
PY - 2010/06/29
Y2 - 2024/08/14
TI - Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms
JF - Journal of Algebraic Statistics
JA - Jalgstat
VL - 1
IS - 1
SE - Articles
DO - 10.29020/nybg.jalgstat.v1i1.7
UR - https://jalgstat.com/index.php/jalgstat/article/view/7
SP - 27-46
AB - <p>This paper presents an efficient group-theoretic approach for computing the statistics of non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographic space groups. In a previous paper we introduced a convolution method for computing the statistics of NRRWs in which the convolution product is defined relative to the space-group operation. Here we use the corresponding concept of the fast Fourier transform for functions on crystallographic space groups together with a non-Abelian version of the convolution theorem. We develop the theory behind this technique and present numerical results for two-dimensional and three-dimensional lattices (square, cubic and diamond). In order to verify our results, the statistics of the end-to-end distance and the probability of ring closure are calculated and compared with results obtained in the literature for the random walks for which closed-form expressions exist.</p>
ER -