Geodesic
Numerical characteristics of groups and the relations between them
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 5-18

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The entropy of the random walk on the discrete contable group could be used for comparison of the system of the generators. Fundamental inequality between growth, entropy and escape gives the possibility to define “the best” system of the generators. We formulate a new circle of the problems related to the various growth and asymptotics on the groups. 
@article{ZNSL_1999_256_a0,
     author = {A. M. Vershik},
     title = {Numerical characteristics of groups and the relations between them},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {256},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a0/}
}
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A. M. Vershik. Numerical characteristics of groups and the relations between them. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 5-18. http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a0/