The KPZ fixed point and Brownian motion share the same null sets on compact intervals.
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Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.
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The KPZ fixed point and Brownian motion share the same null sets
The KPZ fixed point and Brownian motion share the same null sets on compact intervals.
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Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
Spatial increments of the KPZ fixed point with arbitrary compactly supported initial data are quantitatively comparable to Brownian motion on compacts, uniformly, enabling large deviation and entropy results.