An invariance principle for the edge of the branching exclusion process (Q808564)

The authors study a branching exclusion process with state space \(\{0,1\}^ Z\). Particles sitting in the lattice perform nearest neighbour symmetric random walks at rate \(\gamma\) with exclusion interaction - i.e. when a particle attempts to jump over an unoccupied site, the jump is suppressed - and each particle creates at rate \({1\over 2}\) a new particle at each unoccupied nearest neighbour site (in particular, particles which have been created will not disappear). It is shown that, for fixed \(\gamma >0\) and for any initial configuration \(\eta\) such that \(\eta\) (0)\(\neq 0\) and \(\sum_{x>0}\eta (x)<\infty\), under appropriate scaling, the position of the rightmost particle converges to a non-degenerate Brownian motion. The authors also obtain a shape theorem for the process starting with one occupied site.