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退化轨迹公式的概率论解释

Probability-theoretic interpretation of degeneracy locus formulas

Richard Rimanyi

arXiv 2609.06237首次发表:更新:

AI 中文总结

本文用随机有理六顶点模型解释退化轨迹的Schwartz-MacPherson类,完成三种经典类型的稳定SSM理论,将斜类与对称类分别解释为概率和Chebyshev矩。

AI 中文摘要

对称和斜对称映射的退化轨迹的Schwartz-MacPherson类。结合已知的普通线性映射公式,这完成了三种经典类型的稳定SSM理论。我们从概率论角度解释这些公式,即通过随机有理六顶点模型的端点随机划分:斜类对应Maya-dimer事件的概率,对称类对应随机2-核的Chebyshev矩。

英文摘要

Schwartz-MacPherson classes of degeneracy loci of symmetric and skew-symmetric maps. Together with the known formulas for ordinary linear maps, this completes the stable SSM theory for the three classical types. We interpret these formulas probabilistically, in terms of the endpoint random partition of a stochastic rational six-vertex model: the skew classes are probabilities of Maya-dimer events, and the symmetric classes are Chebyshev moments of the random 2-core.

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