AI 中文总结
研究一维两种群对称简单排斥过程与临界缓慢边界储库接触时的非平衡密度涨落，证明耦合涨落场收敛到广义奥恩斯坦 - 乌伦贝克过程，其极限过程由线性鞅问题表征，反映多种因素综合影响。
AI 中文摘要
我们研究了与临界缓慢边界储库接触的一维两种群对称简单排斥过程的非平衡密度涨落。边界速率为$1/n$阶，这在宏观层面导致罗宾边界条件。我们证明与两种群经验密度相关的耦合涨落场收敛到一个广义奥恩斯坦 - 乌伦贝克过程。极限过程由一个线性鞅问题表征，其系数反映了体扩散、物种转换和边界储库的综合影响。
英文摘要
We study the non-equilibrium density fluctuations of a one-dimensional two-species symmetric simple exclusion process in contact with critical slow boundary reservoirs. The boundary rates are of order $1/n$, which leads to Robin boundary conditions at the macroscopic level. We prove that the coupled fluctuation field associated with the empirical densities of two species converges to a generalized Ornstein-Uhlenbeck process. The limiting process is characterized by a linear martingale problem whose coefficients reflect the combined effects of bulk diffusion, species conversion, and the boundary reservoirs.
