Watching a drunkard for 10 nights: A study of distributions of variances

American Journal of Physics

Volumn 71, Issue 9, 2003, Pages 859-865

  Zia, R K P ^a   Schmittmann, B ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041760336     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1566430     Document Type: Article

References (13)

1. B. D. Hughes, Random Walks and Random Environments (Clarendon, Oxford, 1995), Vol. 1.
2. See, for example, F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), Ref. 4.
3. K. Pearson, "The problem of the random walk," Nature (London) 72, 294 (1905); Lord Rayleigh, "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase," Philos. Mag. 10, 73-78 (1880); M. von Smoluchowski, "Zur kinetischen Theorie der Brownschen Mole-kularbewegung und der Suspensionen," Ann. Phys. (Leipzig) 21, 756-780 (1906); G. Pólya, "Wahrscheinlichkeitstheoretisches úber die Irrfahrt," Mitteilungen der Physikalischen Gesellschaft Zürich 19, 75-86 (1919). A brief history of the random walk problem can be found in Ref. 1.
4. K. Pearson, "The problem of the random walk," Nature (London) 72, 294 (1905); Lord Rayleigh, "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase," Philos. Mag. 10, 73-78 (1880); M. von Smoluchowski, "Zur kinetischen Theorie der Brownschen Mole-kularbewegung und der Suspensionen," Ann. Phys. (Leipzig) 21, 756-780 (1906); G. Pólya, "Wahrscheinlichkeitstheoretisches úber die Irrfahrt," Mitteilungen der Physikalischen Gesellschaft Zürich 19, 75-86 (1919). A brief history of the random walk problem can be found in Ref. 1.
5. K. Pearson, "The problem of the random walk," Nature (London) 72, 294 (1905); Lord Rayleigh, "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase," Philos. Mag. 10, 73-78 (1880); M. von Smoluchowski, "Zur kinetischen Theorie der Brownschen Mole-kularbewegung und der Suspensionen," Ann. Phys. (Leipzig) 21, 756-780 (1906); G. Pólya, "Wahrscheinlichkeitstheoretisches úber die Irrfahrt," Mitteilungen der Physikalischen Gesellschaft Zürich 19, 75-86 (1919). A brief history of the random walk problem can be found in Ref. 1.
6. K. Pearson, "The problem of the random walk," Nature (London) 72, 294 (1905); Lord Rayleigh, "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase," Philos. Mag. 10, 73-78 (1880); M. von Smoluchowski, "Zur kinetischen Theorie der Brownschen Mole-kularbewegung und der Suspensionen," Ann. Phys. (Leipzig) 21, 756-780 (1906); G. Pólya, "Wahrscheinlichkeitstheoretisches úber die Irrfahrt," Mitteilungen der Physikalischen Gesellschaft Zürich 19, 75-86 (1919). A brief history of the random walk problem can be found in Ref. 1.
7. H. Gould and J. Tobochnik, Thermal and Statistical Physics, available online at 〈hhttp://stp.clarku.edu/notes〉.
8. H. Gould and J. Tobochnik (private communication).
9. See, for example, NIST/SEMATECH e-Handbook of Statistical Methods, 〈hhttp://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm〉
10. See, for example, M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1974).
11. G. Foltin, K. Oerding, Z. Rácz, R. L. Workman, and R. K. P. Zia, "Width distribution for random-walk interfaces," Phys. Rev. E 50, R639-R642 (1994).
12. D. Ertas and Y. Kantor, "Randomly charged polymers, random walks, and their extremal properties," Phys. Rev. E 53, 846-860 (1996). See the same article for another aspect of this problem, and S. Wolfling and Y. Kantor, "Loops in one-dimensional random walks," Eur. Phys. J. B 12, 569-577 (1999) for other generalizations.
13. D. Ertas and Y. Kantor, "Randomly charged polymers, random walks, and their extremal properties," Phys. Rev. E 53, 846-860 (1996). See the same article for another aspect of this problem, and S. Wolfling and Y. Kantor, "Loops in one-dimensional random walks," Eur. Phys. J. B 12, 569-577 (1999) for other generalizations.