AI 中文总结
研究D型非对称简单排斥过程的长时间渐近性，在固定\(q\) regime利用电流解耦恒等式证明渐近流体动力学极限和Tracy-Widom涨落解耦，在弱不对称 regime证明两个密度涨落场解耦且极限正态随机变量相关，给出相关函数。
AI 中文摘要
D型非对称简单排斥过程是整数集上的一种非对称双物种相互作用粒子系统，其中两个分别守恒的物种跳跃、结合成一个复合“束缚对”并分裂。该模型及其可逆测度和正交多项式对偶性是利用\(U_q(\so_{2n})\)的表示理论构建的。本文研究了D型非对称简单排斥过程的长时间渐近性。在固定\(q\) regime下，利用精确的电流解耦恒等式，证明了渐近流体动力学极限和Tracy-Widom涨落解耦。在弱不对称（Edwards-Wilkinson） regime下，当\(q = 1 - c/N^2\)时，证明了两个密度涨落场解耦，且两个极限正态随机变量相关，相关函数为\((1 - e^{-4c})/(4c)\)。除摘要和引言外，本文由Claude Opus 4.8和Fable 5完成，证明在Lean中形式化，作者手动验证了证明。
英文摘要
The type D ASEP is an asymmetric two--species interacting particle system on $\Z$, in which two separately conserved species hop, bind into a composite ``bound pair'', and split. The model, along with its reversible measures and orthogonal polynomial duality, was constructed using the representation theory of $U_q(\so_{2n})$. The reversible measures and orthogonal polynomial duality are each a product of two copies of the single-species ASEP reversible measures and orthogonal polynomial duality. In this paper, we study the long-time asymptotics of the type D ASEP. In the fixed--$q$ regime, using an exact current--decoupling identity, we prove that the asymptotic hydrodynamic limit and Tracy--Widom fluctuations decouple, as predicted from the duality. In the weak--asymmetry (Edwards--Wilkinson) regime, when $q=1-c/N^2$, we prove that the two density fluctuation fields \underline{decouple}: each converges to a linear stochastic heat equation, with no cross--coupling in either the drift or the noise, the limiting noises having vanishing cross--correlation. More surprisingly, we then prove that the two limiting normal random variables are \underline{correlated} with a seemingly new correlation function. The correlation is exactly equal to $(1-e^{-4c})/(4c)$, with the positive parts of the normal random variables having correlations expressed by the Bessel--Struve function. This paper, with the exception of the abstract and introduction, was written entirely by Claude Opus 4.8 and Fable 5. The proofs were then formalized in Lean, using Aristotle by Harmonic AI. The human author of this paper verified the proofs manually.
Comments46 pages
