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- W2891797989 abstract "The branching number of an arbitrary infinite locally finite tree is, conceptually, the average number of branches extending from a given vertex. A random walk performed on such a tree with known probabilities can be modeled as current flowing through a series of resistors, and vice versa. The arbitrary positive parameter which establishes the canonical choice of resistances is denoted lambda. In Random Walks and Percolation on Trees, Dr. Russell Lyons presents and proves a theorem which states that when lambda is less than the branching number, current flows and the corresponding walk is transient; but when lambda is greater than the branching number, current does not flow and the walk is recurrent. This paper will establish the concepts, tools, and proofs necessary to understand and ultimately prove Lyons's theorem, assuming the reader has no more than undergraduate experience in analysis, probability theory, and basic circuits." @default.
- W2891797989 created "2018-09-27" @default.
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- W2891797989 date "2013-01-01" @default.
- W2891797989 modified "2023-10-17" @default.
- W2891797989 title "Random Walks and Current Flow" @default.
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