Abstract
Random walks on graphs and Markov chains with a finite number of states have been investigated for over 90 years, but their study really took off only in the last two decades or so. The main reasons for this heightened activity are the systematic exploitation of the surprising and extremely useful connection with electrical networks, the emergence of intricate combinatorial arguments, the use of the spectral properties of relevant matrices, and applications of harmonic analysis. In this chapter we shall dip into the theory of random walks on graphs, emphasizing combinatorial arguments, the connection with electrical networks, and eigenvalues.
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© 1998 Springer Science+Business Media New York
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Bollobás, B. (1998). Random Walks on Graphs. In: Modern Graph Theory. Graduate Texts in Mathematics, vol 184. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0619-4_9
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DOI: https://doi.org/10.1007/978-1-4612-0619-4_9
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