Geodesic
Characteristics of random walks on wreath products
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 31-37

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The paper analyses the entropy and the normalised drift of wreath product of finitely generated groups. Examples of groups of zero entropy are given. 
@article{ZNSL_1999_256_a3,
     author = {A. Dubina},
     title = {Characteristics of random walks on wreath products},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {31--37},
     publisher = {mathdoc},
     volume = {256},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a3/}
}
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A. Dubina. Characteristics of random walks on wreath products. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 31-37. http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a3/