First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory
In 1957, Broadbent and Hammersley gave a mathematical formulation of percolation theory. Since then much work has been done in this field and has now led to first-passage percolation problems. In the following two examples we contrast the early formulation with its more recent developments.
KeywordsAdditive Process Percolation Theory Lateral Shift Renewal Theory Nonnegative Random Variable
Unable to display preview. Download preview PDF.
- Doob, J. L.: Stochastic Processes. New York: Wiley 1952.Google Scholar
- Feller, W.: An introduction to probability theory and its applications. New York: Wiley 1957.Google Scholar
- Hammersley, J. M.: Generalization of the fundamental theorem on subadditive functions. Proc. Cambridge Phil. Soc. 58, 235 (1962).Google Scholar
- Hille, E.: Functional Analysis and Semigroups. Amer. Math. Soc. Colloq. Publ. 1957, 31.Google Scholar
- Kochen, M., C. Abraham, and E. Wong: Adaptive man-machine concept-processing. Air Force Cambridge Research Laboratories Report No. 397 (1962).Google Scholar
- Pollack, M.: Solutions of the kth best route through a network — a review. To appear in J. Math. Anal, and Appl.Google Scholar
- Smith, W. L.: Renewal theory and its ramifications. J. Roy. Statist. Soc. B. 20, 243 (1958).Google Scholar