@article{Skliros_Park_Chirikjian_2010, title={Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms}, volume={1}, url={https://jalgstat.com/index.php/jalgstat/article/view/7}, DOI={10.29020/nybg.jalgstat.v1i1.7}, abstractNote={<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>}, number={1}, journal={Journal of Algebraic Statistics}, author={Skliros, Aris and Park, Wooram and Chirikjian, Gregory S.}, year={2010}, month={Jun.}, pages={27–46} }