AI 中文总结
研究二维SSEP在圆形被动计数边界的退火电流涨落，通过径向对称极小值、非等谱公式及散射与因式分解，得到电流大偏差统计的闭式表达式。
AI 中文摘要
我们研究二维对称简单排斥过程（SSEP）在圆形被动计数边界上的退火电流涨落。初始密度为：半径R的圆盘内是ρ₁，圆盘外是ρ₂，观测值为有限时间内圆盘内粒子数的净减少量。利用宏观涨落理论作用量的凸性和旋转平均，我们证明二维变分问题的极小值可选取径向对称形式。对得到的径向问题，合适的变量变换会导出半直线上的非等谱公式。结合相关散射构造与标量因式分解，我们得到标度 cumulant 生成函数的闭式表达式，进而得到电流的退火大偏差统计。
英文摘要
We study annealed current fluctuations in the two-dimensional symmetric simple exclusion process (SSEP) across a circular passive counting boundary. The initial average density is $ρ_1$ inside a disk of radius $R$ and $ρ_2$ outside, and the observable is the net decrease of the particle number in the disk over a finite time. Using convexity of the macroscopic fluctuation theory action and rotational averaging, we show that the minimizer of the full two-dimensional variational problem may be chosen radially symmetric. For the resulting radial problem, a suitable change of variables leads to a nonisospectral formulation on the half-line. Combining the associated scattering construction with a scalar factorization, we obtain a closed expression for the scaled cumulant generating function and hence the annealed large-deviation statistics of the current.
CommentsMore rigorous discussion of the SCGF calculation is provided. A preliminary appendix is included in the source code and will be refined soon
