A signal-recovery system: asymptotic properties and construction of an infinite volume limit
Probability
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0012237,
title = {A signal-recovery system: asymptotic properties and construction of an infinite volume limit},
author = {Jacob van den Berg and Balint Toth},
journal= {arXiv preprint arXiv:math/0012237},
year = {2007}
}
Comments
16 pages