|
1
|
The continuous-time frog model can spread arbitrarily fast. Stat Probab Lett 2021. [DOI: 10.1016/j.spl.2021.109046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
|
2
|
A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site. J THEOR PROBAB 2020. [DOI: 10.1007/s10959-020-01032-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
AbstractWe 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.
Collapse
|