Cannizzaro G, Gonçalves P, Misturini R, Occelli A. From ABC to KPZ.
Probab Theory Relat Fields 2024;
191:361-420. [PMID:
40013018 PMCID:
PMC11850583 DOI:
10.1007/s00440-024-01314-z]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Revised: 06/27/2024] [Accepted: 09/03/2024] [Indexed: 02/28/2025]
Abstract
We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with N ∈ N points, denoted by T N , and with three species of particles that we name A, B and C, but such that at each site there is only one particle. We prove that proper choices of density fluctuation fields (that match those from nonlinear fluctuating hydrodynamics theory) associated to the (two) conserved quantities converge, in the limit N → ∞ , to a system of stochastic partial differential equations, that can either be the Ornstein-Uhlenbeck equation or the Stochastic Burgers equation. To understand the cross interaction between the two conserved quantities, we derive a general version of the Riemann-Lebesgue lemma which is of independent interest.
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