Initial-condition universality of the KPZ upper tail field

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Let the KPZ fixed point have a general initial condition that grows sufficiently more slowly than f(x)=x2f(x)=x^2 as ∣x∣|x| becomes large, so that the KPZ fixed point exists at (0,1)(0,1). General-initial-condition upper-tail conjecture. Theorem 1 holds for the KPZ fixed point with such a general initial condition, and the upper tail field of the KPZ fixed point is independent of the initial condition. This is proposed as a generalization of the paper's main result beyond the narrow-wedge initial condition; the supplied text gives no resolution.

References

Primary source

Zhipeng Liu and Ruixuan Zhang, “An upper tail field of the KPZ fixed point”, arXiv:2501.00932 (2025).

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