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arXiv · 2610.38785

Small-time Wasserstein action for KPZ and $Φ^4_3$

Obayda Julien Assaad
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Abstract

We determine the leading small-time Wasserstein action of the full spatial laws of centered KPZ and dynamical $Φ^4_3$, both started from zero. The leading term is Gaussian, with an explicit heat-trace constant. A common comparison also determines the ratio of length to displacement. For KPZ, a first-chaos cancellation yields a quadratic coupling error. For $Φ^4_3$, two weighted entropies and an adjoint estimate give comparison bounds uniform in the spectral cutoff. Integrating a Gaussian rotation gives a differentiable realization of the full law; the comparison holds at every positive time.

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Obayda Julien Assaad. 2026-10-28. Small-time Wasserstein action for KPZ and $Φ^4_3$. https://arxiv.org/abs/2610.38785

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