Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T23:05:08.330Z Has data issue: false hasContentIssue false
  • English
  • Français

Inclusion-exclusion methods for treating annihilating and deposition processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
∗ Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, Victoria, 3800, Australia. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Annihilationadsorptioninteracting particles

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 466 - 478
Copyright
Copyright © Applied Probability Trust 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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, 223–241.Google Scholar
Evans, J. W. (1993). Random and cooperative adsorption. Rev. Modern Phys. 65, 1281–1329.Google Scholar
Flory, P. J. (1939). Intramolecular reaction between neighboring substituents of vinyl polymers. J. Amer. Chem. Soc. 61, 1518–1521.Google Scholar
Huffer, F. W. (2002). General one-dimensional Poisson growth models with random and asymmetric growth. Preprint. To appear in Methodol. Comput. Appl. Math.Google Scholar
Liggett, T. M. (1985). Interacting Particle Systems. Springer, New York.CrossRefGoogle Scholar
O’Hely, M., and Sudbury, A. W. (2001). The annihilating process. J. Appl. Prob. 38, 223–231.Google Scholar
Page, E. S. (1959). The distribution of vacancies on a line. J. R. Statist. Soc. B 21, 364–374.Google Scholar