Title: Gaussian multiplicative chaos limit of the Brownian loop soup Poisson layering fields.
Speaker: Tulasi Ram Reddy (NYU, Abu-Dhabi)
Date: 06 August 2018
Time: 2.15 pm
Venue: LH-1, Mathematics Department
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 -