Properties of Random Walk on a Tree

Student: Konovalova Adelina

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2017

Properties of random walk on a tree. In the presented graduating paper the properties of a random walk on a tree are explored. The problems of the density of the particle distribution and the number of trajectories of a random walk with a "heavy" root singularity are considered. The aim of the study is to compute the asymptotic characteristics of random walk depending on a tree's topology. Numerical simulation using the transfer-matrix method is performed, analytical results are obtained in two ways: by analyzing the spectrum of the tree contiguity matrix and using the method of generating functions. As a result of the work, it was found that in the problem of the number of trajectories of a random walk on a tree, unlike the random walk problem, it is possible to localize a trajectory near the "heavy" root. Localization conditions are established.

Full text (added May 25, 2017)

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