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Small-time Wasserstein action for KPZ and Φ43
Abstract
We determine the leading small-time Wasserstein action of the full spatial laws of centered KPZ and dynamical Φ43, 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 Φ43, 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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BibTeX
@misc{assaad2026smalltime,
title = {{Small-time Wasserstein action for KPZ and $Φ^4_3$}},
author = {Obayda Julien Assaad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38785},
eprint = {2610.38785},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38785},
}
RIS
TY - UNPB
TI - Small-time Wasserstein action for KPZ and Φ^4_3
AU - Obayda Julien Assaad
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38785
UR - https://arxiv.org/abs/2610.38785
AB - 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.
ER -