## Random walks with internal degrees of freedom. I: Local limit theorems.(English)Zbl 0494.60067

### MSC:

 60G50 Sums of independent random variables; random walks 60F05 Central limit and other weak theorems 60K35 Interacting random processes; statistical mechanics type models; percolation theory

### Citations:

Zbl 0038.290; Zbl 0203.502
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### References:

 [1] Bhattacharya, R. N.; Ranga Rao, R., Normal Approximation & Asymptotic Expansions (1976), New York: Wiley-Interscience, New York · Zbl 0331.41023 [2] Bunimovich, L. A.; Sinai, Ya. G., Markov partitions for dispersed billiards, Comm. Math. Phys., 78, 247-280 (1981) · Zbl 0453.60098 [3] Bunimovich, L. A.; Sinai, Ya. G., Statistical properties of Lorentz gas with periodic configuration of scatters, Comm. Math. Phys., 78, 479-497 (1981) · Zbl 0459.60099 [4] Feller, W., An Introduction to Probability Theory and its Applications. Volume II (1966), New York: Wiley, New York · Zbl 0138.10207 [5] Friedrichs, K.O.: Perturbation of Spectra in Hilbert Space. Providence: Amer. Math. Soc. 1965 · Zbl 0142.11001 [6] Gantmacher, F. R., Theory of Matrices (1967), Moscow: Nauka, Moscow · Zbl 0085.01001 [7] Ibragimov, I. A.; Linnik, Yu. V., Independent and Stationarily Depending Variables (In Russian) (1965), Moscow: Nauka, Moscow · Zbl 0154.42201 [8] Kato, T., Perturbation Theory for Linear Operators (1980), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York [9] Sinai, Ya.G.: Random walks and some problems concerning Lorentz gas. Proceedings of the Kyoto Conference. 6-17 (1981) [10] Kolmogorov, A. N., A local limit theorem for classical Markov chains, Izvesti’a Akad. Nauk SSSR. Ser. mat., 13, 281-300 (1949) [11] Statulevicius, V. A., Limit theorems for sums of random variables connected through a Markov chain, Lietuvos Mat. Rinkinys, 9, 346-362 (1969)
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