A general linear birth and growth model (Q2713155)

The authors consider a birth and growth model where points (`seeds') arrive on a line randomly in time and space and proceed to `cover' the line by growing at a uniform rate in both directions until an opposing branch is met; points which arrive on covered parts of the line do not contribute to the process. They are interested in the number \(N(L)\) of seeds formed by the time an interval \([0,L]\) is covered. Existing results concerning \(N(L)\) assume that points arrive according to a Poisson process, homogeneous on the line, but possibly inhomogeneous in time. The authors' results are derived under less stringent assumptions, namely that the arrival process is a stationary simple point process.