an:02138909
Zbl 1058.60093
van den Berg, J.; T??th, B.
A signal-recovery system: asymptotic properties, and construction of an infinite-volume process
EN
Stochastic Processes Appl. 96, No. 2, 177-190 (2001).
00091898
2001
j
60K35 82C43 92D25
on-off sequence; long-range interactions; infinite-volume dynamics; 1-D time-dependent percolation
Summary: We consider a linear sequence of `nodes', each of which can be in state 0 (`off') or 1 (`on'). Signals from outside are sent to the rightmost node and travel instantaneously as far as possible to the left along nodes which are `on'. These nodes are immediately switched off, and become on again after a recovery time. The recovery times are independent exponentially distributed random variables. We present results for finite systems and use some of these results to construct an infinite-volume process (with signals `coming from infinity'), which has some peculiar properties. This construction is related to a question by D. Aldous and we hope that it sheds some light on, and stimulates further investigation of, that question.