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August, 1974 Postulates for Subadditive Processes
J. M. Hammersley
Ann. Probab. 2(4): 652-680 (August, 1974). DOI: 10.1214/aop/1176996611


The paper examines alternative postulates for subadditive processes, especially the ergodic theory thereof. It introduces superconvolutive sequences of distributions and proves limit laws for these, which generalize the weak law of large numbers, Chernoff's theorem, and Kesten's lemma. It discusses eigenshift and eigendistribution theory and concave recurrence relations in the convolutive semigroup, illustrating sundry conjectures with computer studies. It deals with applications of the theory to the first-death problem in branching processes, Bethe approximation of first-passage percolation, self-avoiding walks, maximal solutions of the generalized subconvolutive inequality, rates of convergence of a subadditive process, multidimensional subadditive processes in physics including the dimer problem and the overlapping-sphere model of liquid-vapor equilibrium, and Ulam's problem on the longest monotone subsequence of a random permutation.


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J. M. Hammersley. "Postulates for Subadditive Processes." Ann. Probab. 2 (4) 652 - 680, August, 1974.


Published: August, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60044
MathSciNet: MR370721
Digital Object Identifier: 10.1214/aop/1176996611

Primary: 60G99
Secondary: 60F10 , 60J85 , 82A05

Keywords: branching process , dimer problem , eigenshifts , ergodic theory , first-death , first-passage , limit laws , liquid-vapor equilibrium , percolation process , self-avoiding walks , superconvolutive sequence , Sybadditive process

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 4 • August, 1974
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