A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site

Viktor Bezborodov (), Luca Persio () and Tyll Krueger ()
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Viktor Bezborodov: Wrocław University of Science and Technology
Luca Persio: The University of Verona
Tyll Krueger: Wrocław University of Science and Technology

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2265-2284

Abstract: 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 limit estimate and an exponential estimate on the fluctuations of the position of the rightmost particle.

Keywords: Birth process; Shape theorem; Interacting particle system; 60K35; 82C22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01032-x

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