BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Titus Lupu (CNRS and Sorbonne Université) DTSTART:20210924T163000Z DTEND:20210924T173000Z DTSTAMP:20260423T005712Z UID:PatC/43 DESCRIPTION:Title: Mu ltiplicative chaos of the 2D Brownian loop soup\nby Titus Lupu (CNRS a nd Sorbonne Université) as part of Probability and the City Seminar\n\n\n Abstract\nIt is known from the works in Mathematical Physics that the cont inuum Gaussian free field (GFF) admits representations in terms of occupat ion measures of Brownian trajectories. In particular\, the square of the G FF (suitably renormalized) has the same distribution as the occupation mea sure of a Poisson point process of Brownian loops\, known as the Brownian loop soup. This is the Le Jan's isomorphism theorem. The Brownian loop sou ps come with an intensity parameter $\\theta >0$\, and the connection to t he GFF is for the particular parameter $\\theta=1/2$. In our work we relat ed the theory of the Gaussian Multiplicative Chaos (GMC) in 2D (renormaliz ed exponential of the 2D continuum GFF\, also appearing in Liouville field theory) to the 2D Brownian loop soup. Actually we constructed a so called multiplicative chaos of the Brownian loop soup for every intensity parame ter $\\theta$. Compared to the multiplicative chaos of a single 2D Brownia n trajectory\, which has been first constructed by Bass\, Burdzy and Khosh nevisan in the 90s\, in our work we require an additional layer of renorma lization due to ultraviolet divergence in the Brownian loop soup. For the particular parameter $\\theta=1/2$\, our multiplicative chaos of the Brown ian loop soup has the same distribution as the renormalized hyperbolic cos ine of the GFF\, i.e. is a sum of two GMCs. For other intensity parameters $\\theta$ we obtain new non-Gaussian multiplicative chaoses\, which satis fy moreover a covariance property under conformal transformations of the d omain. This is joint work with Elie Aïdekon (Sorbonne Université/Fudan U niversity)\, Nathanael Berestycki (University of Vienna) and Antoine Jégo (University of Vienna).\n LOCATION:https://researchseminars.org/talk/PatC/43/ END:VEVENT END:VCALENDAR