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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.