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- W175598629 abstract "Different models of generating random regular graphs have been widely studied, such as the configuration model, the d-process and the d-star process. We will have a brief overview of properties of these models. We will also review properties of Markov chains, and the coupling method, which is usually used to prove the mixing rate of a Markov chain. In this essay, we study a new algorithm, called pegging, to generate random d-regular graphs. We prove that the number of triangles has a limiting Poisson distribution, and estimate the rate at which it approaches its limiting distribution. The method we used is similar to the coupling method, but we will first extend the coupling lemma, so that we can measure the total variation distance between two random processes, instead of two copies of a same Markov chain. Therefore the case we study here is quite different from that we usually see in Markov chains. We conjecture this result also holds for k-cycle for any fixed k, and more precisely, the number of k-cycles, where k = 3,4,5, . . . are asymptotically independent Poisson random variables." @default.
- W175598629 created "2016-06-24" @default.
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- W175598629 date "2006-01-01" @default.
- W175598629 modified "2023-09-27" @default.
- W175598629 title "Models of generating random regular graphs and their short cycle distribution" @default.
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