International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 683-688
doi:10.1155/S0161171285000758
Random walk over a hypersphere
Shipra Sadan, G. I. C. Road, Pittogarab, U. P. 262501, India
Received 10 November 1983; Revised 23 July 1985
Copyright © 1985 J. M. C. Joshi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In a recent paper the author had shown that a special case of S. M. Joshi
transform (so named after the author's reverent father) of distributions
(Sba f)(x)=〈f(y), lFl(a0;b0;ixy) lFl(a;b;−2ixy)〉
is a characteristic function of a spherical distribution. Using the methods developed in that paper; the problem of distribution of the distance CD, where C and D are points niformly distributed in a hypersphere, has been discussed in the present paper. The form of characteristic function has also been obtained by the method of projected distribution.
A generalization of Hammersley's result has also been developed. The main purpose of the paper is to show that although the use of characteristic functions, using the method of Bochner, is available in problems of random walk yet distributional S. M. Joshi transform can be used as a natural tool has been proved for the first time in the paper.