Information Transmission and Criticality in the Contact Process
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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.
KeywordsContact process Criticality Information transmission Duality and coupling
Mathematics Subject Classification60K35 82B27
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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