Abstract
In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter \(\lambda .\) We introduce a notion of sensitivity of the process to its initial condition and prove that it increases not only for values of \(\lambda < \lambda _c, \) the value of the critical parameter, but keeps increasing even after \( \lambda _c , \) before finally starting to decrease for values of \(\lambda \) sufficiently above \(\lambda _c.\) This provides a counterexample to the common belief that associates maximal information transmission to criticality.
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29 November 2017
The original publication of the article unfortunately contained a mistake in the first sentence of Theorem 1 and in the second part of the proof of Theorem 1. The corrected statement of Theorem as well as the corrected proof are given below. The full text of the corrected version is available at http://arxiv.org/abs/1705.11150
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Acknowledgements
Many thanks to Errico Presutti and Antonio Carlos Roque da Silva Filho for stimulating discussions about this subject. We also thank two anonymous referees for helpful comments and suggestions. We thank the Gran Sasso Science Institute (GSSI) for hospitality and support. This research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01), USP project Mathematics, computation, language and the brain and FAPESP project Research, Innovation and Dissemination Center for Neuromathematics (Grant 2013/07699-0). AG is partially supported by CNPq fellowship (Grant 311 719/2016-3.)
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A correction to this article is available online at https://doi.org/10.1007/s10955-017-1931-7.
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Cassandro, M., Galves, A. & Löcherbach, E. Information Transmission and Criticality in the Contact Process. J Stat Phys 168, 1180–1190 (2017). https://doi.org/10.1007/s10955-017-1854-3
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DOI: https://doi.org/10.1007/s10955-017-1854-3