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Forest fire model on ℤ+ with delays

Bhattacharya, Satyaki LU and Volkov, Stanislav LU orcid (2026) In Journal of Applied Probability
Abstract

We consider a generalization of the forest fire model on ℤ+ with ignition at zero only, studied by Volkov (2009 ALEA 6, 399–414). Unlike that model, we allow delays in the spread of the fires and the non-zero burning time of individual ‘trees’. We obtain some general properties for this model, which cover, among others, the phenomenon of an ‘infinite fire’, not present in the original model.

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author
and
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Forest fire models, interacting particle systems
in
Journal of Applied Probability
publisher
Applied Probability Trust
external identifiers
  • scopus:105030043800
ISSN
0021-9002
DOI
10.1017/jpr.2025.10040
language
English
LU publication?
yes
id
e953258a-2481-4e80-9208-b73d7bef56bb
date added to LUP
2026-03-02 13:45:41
date last changed
2026-03-02 13:46:43
@article{e953258a-2481-4e80-9208-b73d7bef56bb,
  abstract     = {{<p>We consider a generalization of the forest fire model on ℤ<sub>+</sub> with ignition at zero only, studied by Volkov (2009 ALEA 6, 399–414). Unlike that model, we allow delays in the spread of the fires and the non-zero burning time of individual ‘trees’. We obtain some general properties for this model, which cover, among others, the phenomenon of an ‘infinite fire’, not present in the original model.</p>}},
  author       = {{Bhattacharya, Satyaki and Volkov, Stanislav}},
  issn         = {{0021-9002}},
  keywords     = {{Forest fire models; interacting particle systems}},
  language     = {{eng}},
  publisher    = {{Applied Probability Trust}},
  series       = {{Journal of Applied Probability}},
  title        = {{Forest fire model on ℤ<sub>+</sub> with delays}},
  url          = {{http://dx.doi.org/10.1017/jpr.2025.10040}},
  doi          = {{10.1017/jpr.2025.10040}},
  year         = {{2026}},
}