Asymptotics of a dynamic random walk in a random scenery : I. Law of large numbers

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1. [1] Baker A., On some diophantine inequalities involving the exponential function, Canad. J. Math.17 (1965) 616-626. Zbl0147.30901MR177946
2. [2] Bolthausen E., A central limit theorem for two-dimensional random walks in random sceneries, Ann. Probab.17 (1) (1989) 108-115. Zbl0679.60028MR972774
3. [3] Guillotin N., Dynamic random walk in a random scenery, C. R. Acad. Sci. Paris Série I 324 (1997) 231-234. Zbl0880.60071MR1438390
4. [4] Guillotin N., Asymptotics of a dynamic random walk in a random scenery: II. A functional limit theorem, Markov Processes and Related Fields, to appear. Zbl0947.60059MR1762173
5. [5] Hof A., Quasicrystals, aperiodicity and lattice systems, Doctoral Dissertation, Rijksuniversiteit, Groningen, 1992. 
6. [6] Kesten H., Spitzer F., A limit theorem related to a new class of self-similar processes, Z. Wahrsch. Verw. Gebiete50 (1979) 5-25. Zbl0396.60037MR550121
7. [7] Khinchin A., Continued Fractions, Chicago University Press, 1964. Zbl0117.28601MR161833
8. [8] Koukiou F., Petritis D., Zahradník M., Extension of the Pirogov-Sinai theory to a class of quasiperiodic interactions, Comm. Math. Phys.118 (1988) 365-383. Zbl0668.58013MR958802
9. [9] Kuipers L., Niederreiter H., Uniform Distribution of Sequences, Wiley, 1974. Zbl0281.10001MR419394
10. [10] Lapeyre B., Pagès G., Familles de suites à discrépance faible obtenues par itérations de transformations de [0, 1], C. R. Acad. Sci. Paris Série I 308 (1989) 507-509. Zbl0676.10038MR998641
11. [11] Ledrappier F., Systèmes Dynamiques, Presses de l'École Polytechnique, 1994. 
12. [12] Lin M., Rubshtein B., Wittmann R., Limit theorems for random walks with dynamical random transitions, Probab. Theory Related Fields100 (1994) 285-300. Zbl0815.60064MR1305584
13. [13] Osgood F.C., Diophantine Approximation and its Applications, Academic Press, 1973. Zbl0254.00006
14. [ 14] Pagès G., Xiao Y.J., Sequences with low discrepancy and pseudo-random numbers: theoretical remarks and numerical tests, Prepublication, 1991. 
15. [15] Schmidt W.M., Simultaneous approximation to algebraic numbers by rationals, Acta Math.125 (1970) 189-201. Zbl0205.06702MR268129
16. [16] Solomon F., Random walks in a random environment, Ann. Probab.3 (1) (1975) 1-31. Zbl0305.60029MR362503
17. [17] Spitzer F., Principles of Random Walk, 2nd ed., Springer, New York, 1976. Zbl0359.60003