AI 中文总结
本文在有限路径图上建立反射与Szegedy游走的局部Konno-Sato对应，通过广义反射原理得到zeta分解，并在对称与非对称情形下恢复经典公式及大质量狄拉克型极限。
AI 中文摘要
我们在有限路径图上建立了反射随机游走和Szegedy游走的局部Konno-Sato对应。一个广义反射原理，在非对称情形下使用显式对合而非点反射，得到了精确的zeta分解，分解为边界因子和由无限二面体群索引的局部因子。在对称化之后，经典和量子局部因子对每个群元素相对应。恒等贡献决定了归一化的热力学极限。在对称情形下，扩散和弹道标度分别恢复了高斯泊松求和公式和狄拉克梳恒等式。在不对称性和谱参数的双重标度下，量子分解产生了一个大质量狄拉克型极限：非恒等偶词产生周期轨道因子，恒等词产生自由场因子，奇词与边界一起产生有限边界修正。
英文摘要
We establish a local Konno-Sato correspondence for reflected random and Szegedy walks on a finite path graph. A generalized reflection principle, using explicit involutions rather than point reflections in the asymmetric case, yields exact zeta factorizations into a boundary factor and local factors indexed by the infinite dihedral group. After symmetrization, the classical and quantum local factors correspond for each group element. The identity contribution determines the normalized thermodynamic limits. In the symmetric case, diffusive and ballistic scalings recover the Gaussian Poisson summation formula and the Dirac comb identity, respectively. Under a double scaling of the asymmetry and spectral parameter, the quantum factorization yields a massive Dirac-type limit: nonidentity even words produce the periodic-orbit factor, the identity produces the free-field factor, and odd words together with the boundary produce a finite boundary correction.
Comments58 pages
