01-25 Jacob van den Berg, Balint Toth

A signal-recovery system: asymptotic properties, and construction of an infinite-volume limit (467K, Postscript) Jan 15, 01

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Abstract. 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 properties for finite systems and use some of these properties to construct an infinite-volume extension, with signals `coming from infinity'. This construction is related to a question by D. Aldous and we expect that it sheds some light on, and stimulates further investigation of, that question.

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