Geodesic
About the power law of the PageRank vector distribution. Part~1. Numerical methods for finding the PageRank vector
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 359-378

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In Part 1 of this paper, we consider the web-pages ranking problem also known as the problem of finding the PageRank vector or Google problem. We discuss the connection of this problem with the ergodic theorem and describe different numerical methods to solve this problem together with their theoretical background, such as Markov Chain Monte Carlo and equilibrium in a macrosystem. 
@article{SJVM_2017_20_4_a1,
     author = {A. Gasnikov and E. Gasnikova and P. Dvurechensky and A. Mohammed and E. Chernousova},
     title = {About the power law of the {PageRank} vector distribution. {Part~1.} {Numerical} methods for finding the {PageRank} vector},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {359--378},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a1/}
}
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A. Gasnikov; E. Gasnikova; P. Dvurechensky; A. Mohammed; E. Chernousova. About the power law of the PageRank vector distribution. Part~1. Numerical methods for finding the PageRank vector. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 359-378. http://geodesic.mathdoc.fr/item/SJVM_2017_20_4_a1/