The limit distribution of Sinai’s random walk in random environment. (English) Zbl 0666.60065
Recently Sinai proved that if \(\{X_ n\}\) is a one-dimensional random walk in random environment which is recurrent, then (log n)\({}^{-2}X_ n\) converges in distribution. Here we calculate the limit distribution explicitly.
MSC:
| 60G50 | Sums of independent random variables; random walks |
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 60F05 | Central limit and other weak theorems |
References:
| [1] | Sinai, Ya. G., Theory Prob. Appl., 27, 256 (1982) · Zbl 0505.60086 |
| [2] | Nauenberg, M., J. Stat. Phys., 41, 803 (1985) |
| [3] | Billingsley, P., Convergence of Probability Measures (1968), Wiley: Wiley New York · Zbl 0172.21201 |
| [4] | Whitt, W., Ann. Math. Statist., 41, 939 (1970) · Zbl 0203.50501 |
| [5] | Feller, W., (An Introduction to Probability Theory and its Applications, Vol. I (1968), Wiley: Wiley New York) · Zbl 0155.23101 |
| [6] | Whittaker, E. T.; Watson, G. N., A Course of Modern Analysis (1952), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0108.26903 |
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