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Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site
- Source :
- Journal of Theoretical Probability volume 34, pages 2265-2284, 2021
- Publication Year :
- 2019
-
Abstract
- We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also derive a limiting estimate and an exponential estimate on the fluctuations of the position of the rightmost particle.<br />Comment: 17 pages; a short section devoted to numerical simulations is added; other small changes and improvements
- Subjects :
- Mathematics - Probability
60K35, 82C22
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Theoretical Probability volume 34, pages 2265-2284, 2021
- Publication Type :
- Report
- Accession number :
- edsarx.1911.12867
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10959-020-01032-x