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Layering fields and Winding fields from loop soups

Dr. Tulasi Ram Reddy NYU Abu Dhabi
Speaker
Dr. Tulasi Ram Reddy NYU Abu Dhabi
When Feb 12, 2019
from 04:00 PM to 05:00 PM
Where LH006
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Abstract:  In the first part we consider winding field obtained from random walk loop soup (RWLS) defined on finite lattice indexed by index by parameters λ and β. We show that there is a Gaussian field limit as the intensity λ of the RWLS diverges and β goes to 0 such that λβ2 is constant. We compute the co-variance kernel of this Gaussian field. We also establish a non-commutative version of the similar result.

In the second part we consider the primary Brownian loop soup (BLS) layering vertex fields index by parameters λ and β. We show the existence of the fields in smooth bounded domains for a suitable range of parameters β's. The BLS layering vertex fields are not free, which is to say they are not the exponential of Gaussians. On the other hand, we use Weiner-Ito chaos expansion to establish that the λ−β2 limit as the intensity λ of the BLS diverges and βgoes to 0 such that λβ2 is constant, is a complex Gaussian multiplicative Chaos.

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