Abstract
Condensing zero range processes are interacting particle systems with zero range interaction exhibiting phase separation at densities above a finite critical density. We prove the hydrodynamic limit of mean zero condensing zero range processes with bounded local jump rate for sub-critical initial profiles, i.e. for initial profiles that are everywhere strictly below the critical density. The proof is based on H.T. Yau’s relative entropy method and is made possible by a generalisation of the one block estimate.
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Acknowledgments
The current research has been co-financed by the European Union (European Social Fund- ESF) and by national resources through the operational programme “Education and Lifelong Learning” of the National Strategic Research Frame (NSRF)—Financed Research Project: Herakleitos II. Investment in the society of knowledge through the European Social Fund.
I am thankful to my advisor Michail Loulakis for his continuous help and encouragement and to Claudio Landim for useful conversations. I would also like to thank the anonymous referees, whose insightful points led to the concluding remarks on the sub-criticality assumption.
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Stamatakis, M.G. Hydrodynamic Limit of Mean Zero Condensing Zero Range Processes with Sub-Critical Initial Profiles. J Stat Phys 158, 87–104 (2015). https://doi.org/10.1007/s10955-014-1113-9
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DOI: https://doi.org/10.1007/s10955-014-1113-9