Quasi-geodesics in integrable and non-integrable exclusion processes

Patrik L. Ferrari; Min Liu

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arXiv · 2412.11626

Quasi-geodesics in integrable and non-integrable exclusion processes

Patrik L. Ferrari·Min Liu

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Abstract

Backwards geodesics for TASEP were introduced in [Fer18]. We consider flat initial conditions and show that under proper scaling its end-point converges to maximizer argument of the Airy$_2$ process minus a parabola. We generalize its definition to generic non-integrable models including ASEP and speed changed ASEP (call it quasi-geodesics). We numerically verify that its end-point is universal, where the scaling coefficients are analytically computed through the KPZ scaling theory.

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Patrik L. Ferrari, Min Liu. 2024-12-16. Quasi-geodesics in integrable and non-integrable exclusion processes. https://arxiv.org/abs/2412.11626

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