Abstract
Equations are derived for the probability of n visits to a given state during the course of a random walk on a finite diagram that starts from a specified state and ends with absorption. By deriving the mean number of visits in two different ways, certain conjectures or theorems are encountered that connect properties of different but related diagrams in an interesting way. Other subjects included are (i) number of one-way transitions between two states before absorption; (ii) time dependence of the rate of cycle completions before absorption; and (iii) the relation of this work to the "return process" of Karlin and Taylor.
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Hill T. L. Further properties of random walks on diagrams (graphs) with and without cycles. Proc Natl Acad Sci U S A. 1988 May;85(10):3271–3275. doi: 10.1073/pnas.85.10.3271. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hill T. L. Interrelations between random walks on diagrams (graphs) with and without cycles. Proc Natl Acad Sci U S A. 1988 May;85(9):2879–2883. doi: 10.1073/pnas.85.9.2879. [DOI] [PMC free article] [PubMed] [Google Scholar]