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A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS

  • JONATHAN M. BORWEIN (a1) and CORWIN W. SINNAMON (a2)
Abstract

We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

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sinncore@gmail.com
References
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[1]Borwein, J. M., Straub, A. and Vignat, C., ‘Densities of short uniform random walks in higher dimensions’, submitted for publication, 2015. Preprint, arXiv:1508.04729.
[2]Borwein, J. M., Straub, A., Wan, J. and Zudilin, W., ‘Densities of short uniform random walks’, Canad. J. Math. 64(5) (2012), 961990; with an Appendix by Don Zagier.
[3]García-Pelayo, R., ‘Exact solutions for isotropic random flights in odd dimensions’, J. Math. Phys. 53(10) 103504 (2012), 67.
[4]Hughes, B. D., Random Walks and Random Environments, Vol. 1, in: Random Walks (Clarendon Press, Oxford, 1995). See, in particular, pages 53–73 and 86–93.
[5]Kluyver, J. C., ‘A local probability problem’, Nederl. Acad. Wetensch. Proc. 8 (1906), 341350.
[6]Pearson, K., ‘A mathematical theory of random migration’, in: Drapers Company Research Memoirs, Biometric Series, 3 (Dulau and Company, London, 1906), 424.
[7]Rayleigh, L., ‘On the problem of random vibrations, and of random flights in one, two, or three dimensions’, Phil. Mag. Ser. 6 37(220) (1919), 321347.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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