We consider the primary Brownian loop soup (BLS) layering vertex fields and show the existence of the fields in smooth bounded domains for a suitable range of parameters $\beta$’s. To show this at a fixed cutoff, we use Kahane’s theory of Gaussian multiplicative chaos. On the other hand, when the cutoff is removed, we use Weiner-Ito chaos expansion to establish that the $\lambda-\beta^2$ limit as the intensity $\lambda$ of the BLS diverges and $\beta$ goes to 0 such that $\lambda\beta^2$ is constant, is a complex Gaussian multiplicative Chaos. Based on joint work with F. Camia, A. Gandolfi and G. Peccati.

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Last updated: 13 Jun 2024