Geodesic
Random walks on plane crystallographic groups
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 204-218
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For the example of the group $G=pgg$ generated by two orthogonal gliding symmetries, we calculate the generating matrix. For the same example, we reduce the property of random walks on planar crystallographic groups to the local behavior of the resolvent. 
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     title = {Random walks on plane crystallographic groups},
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     year = {2001},
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     language = {ru},
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V. G. Zhuravlev; A. A. Yudin. Random walks on plane crystallographic groups. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 204-218. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a8/