PreprintCC BY-NC-ND 4.0HAL
Derivatives of Gaussian multiplicative chaos
Abstract
Consider a logarithmically-correlated Gaussian field in any dimension d. For all γ ∈ (-√ 2d, √ 2d), we show that the derivatives of the regularised Gaussian multiplicative chaos converge as the regularisation parameter is sent to 0. By deriving optimal bounds on their growth, we control the power expansion of the regularised GMC about each γ ∈ (-√ 2d, √ 2d). This yields an alternative approach to complex Gaussian multiplicative chaos in the whole subcritical regime, based entirely on real-valued quantities. One of our key technical contributions is to provide a truncated second moment approach to the uniform integrability of the derivatives of multiplicative chaos and its associated complex variant.
Related
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- Critical Gaussian Multiplicative Chaos on the Circle Is Rajchman
BibTeX
@misc{jego2026derivatives,
title = {{Derivatives of Gaussian multiplicative chaos}},
author = {Antoine Jego},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05765149v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Derivatives of Gaussian multiplicative chaos
AU - Antoine Jego
PY - 2026
DA - 2026/09/25
PB - HAL
UR - https://hal.science/hal-05765149v1
AB - Consider a logarithmically-correlated Gaussian field in any dimension d. For all γ ∈ (-√ 2d, √ 2d), we show that the derivatives of the regularised Gaussian multiplicative chaos converge as the regularisation parameter is sent to 0. By deriving optimal bounds on their growth, we control the power expansion of the regularised GMC about each γ ∈ (-√ 2d, √ 2d). This yields an alternative approach to complex Gaussian multiplicative chaos in the whole subcritical regime, based entirely on real-valued quantities. One of our key technical contributions is to provide a truncated second moment approach to the uniform integrability of the derivatives of multiplicative chaos and its associated complex variant.
ER -