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September 2016 >Bit flipping and time to recover
Anton Muratov, Sergei Zuyev
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J. Appl. Probab. 53(3): 650-666 (September 2016).

Abstract

We call `bits' a sequence of devices indexed by positive integers, where every device can be in two states: 0 (idle) and 1 (active). Start from the `ground state' of the system when all bits are in 0-state. In our first binary flipping (BF) model the evolution of the system behaves as follows. At each time step choose one bit from a given distribution P on the positive integers independently of anything else, then flip the state of this bit to the opposite state. In our second damaged bits (DB) model a `damaged' state is added: each selected idling bit changes to active, but selecting an active bit changes its state to damaged in which it then stays forever. In both models we analyse the recurrence of the system's ground state when no bits are active. We present sufficient conditions for both the BF and DB models to show recurrent or transient behaviour, depending on the properties of the distribution P. We provide a bound for fractional moments of the return time to the ground state for the BF model, and prove a central limit theorem for the number of active bits for both models.

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Anton Muratov. Sergei Zuyev. ">Bit flipping and time to recover." J. Appl. Probab. 53 (3) 650 - 666, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60104
MathSciNet: MR3570086

Subjects:
Primary: 60J27
Secondary: 60J10 , 68Q87

Keywords: Binary system , bit flipping , critical behaviour , Markov chain recurrence , Random walk on a group

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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