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Inclusion-exclusion methods for treating annihilating and deposition processes

  • Aidan Sudbury (a1)

Abstract

We consider one-dimensional processes in which particles annihilate their neighbours, grow until they meet their neighbours or are deposited onto surfaces. All of the models considered have the property that they are connected to exponential series often by an inclusion-exclusion argument.

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Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, Victoria, 3800, Australia. Email address: aidan.sudbury@sci.monash.edu.au

References

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Daley, D. J., Mallows, C. L., and Shepp, L. A. (2000). A one-dimensional Poisson growth model with non-overlapping intervals. Stoch. Process. Appl. 90, 223241.
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Flory, P. J. (1939). Intramolecular reaction between neighboring substituents of vinyl polymers. J. Amer. Chem. Soc. 61, 15181521.
Huffer, F. W. (2002). General one-dimensional Poisson growth models with random and asymmetric growth. Preprint. To appear in Methodol. Comput. Appl. Math.
Liggett, T. M. (1985). Interacting Particle Systems. Springer, New York.
O’Hely, M., and Sudbury, A. W. (2001). The annihilating process. J. Appl. Prob. 38, 223231.
Page, E. S. (1959). The distribution of vacancies on a line. J. R. Statist. Soc. B 21, 364374.

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Inclusion-exclusion methods for treating annihilating and deposition processes

  • Aidan Sudbury (a1)

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