Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site

Viktor Bezborodov; Luca Di Persio; Tyll Krueger

doi:10.1007/s10959-020-01032-x

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arXiv · 1911.12867

Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site

Viktor Bezborodov·Luca Di Persio·Tyll Krueger

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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.

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Viktor Bezborodov, Luca Di Persio, Tyll Krueger. 2020-07-14. Shape theorem for a one-dimensional growing particle system with a bounded number of occupants per site. https://doi.org/10.1007/s10959-020-01032-x

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