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 '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 limit as the intensity of the BLS diverges and goes to 0 such that is constant, is a complex Gaussian multiplicative Chaos. ( Based on joint work with F. Camia, A. Gandolfi and G. Peccati)
Gaussian multiplicative chaos limit of the Brownian loop soup Poisson layering fields.