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Hydrodynamics of a class of N-urn linear systems

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  • Xue, Xiaofeng

Abstract

In this paper we are concerned with hydrodynamics of a class of N-urn linear systems, which include voter models, pair-symmetric exclusion processes and binary contact path processes on N urns as special cases. We show that the hydrodynamic limit of our process is driven by a C[0,1)′-valued linear ordinary differential equation and the fluctuation of our process, i.e, central limit theorem from the hydrodynamic limit, is driven by a C[0,1)′-valued Ornstein–Uhlenbeck process. To derive above main results, we need several replacement lemmas. An extension in linear systems of Chapman–Kolmogorov equation plays key role in proofs of these replacement lemmas.

Suggested Citation

  • Xue, Xiaofeng, 2023. "Hydrodynamics of a class of N-urn linear systems," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 69-100.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:69-100
    DOI: 10.1016/j.spa.2022.11.007
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    References listed on IDEAS

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    1. Xue, Xiaofeng & Zhao, Linjie, 2020. "Hydrodynamics of the weakly asymmetric normalized binary contact path process," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6757-6782.
    2. Xue, Xiaofeng & Zhao, Linjie, 2021. "Non-equilibrium fluctuations of the weakly asymmetric normalized binary contact path process," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 227-253.
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    1. Xue, Xiaofeng & Zhao, Linjie, 2021. "Non-equilibrium fluctuations of the weakly asymmetric normalized binary contact path process," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 227-253.

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