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arXiv · 2510.22165

The real layering field of Brownian loop soup and the Gaussian multiplicative chaos

Sayantan Maitra
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Abstract

We consider the random field defined by the layering numbers of the Brownian loop soup in a bounded simply connected domain in the complex plane. We call this the layering field and show that, after a suitable renormalization, it converges to the subcritical Gaussian multiplicative chaos. The main technique for our proof is the Wiener-It\^{o} chaos expansion. We also calculate the $n$-point functions of the layering field, show their conformal covariance and discuss their behavior near the boundary of the domain.

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Sayantan Maitra. 2025-10-25. The real layering field of Brownian loop soup and the Gaussian multiplicative chaos. https://arxiv.org/abs/2510.22165

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