Multiplicative chaos of the Brownian loop soup

We construct a measure on the thick points of Brownian loop soup in bounded domain D $D$ plane with given intensity θ > 0 $\theta >0$ , which is formally obtained by exponentiating square root its occupation field. The constructed via regularisation procedure, loops are killed at fix rate, allowing us to make use multiplicative chaos measures previously considered Aïdékon et al. (Ann. Probab. 48 (2020), no. 4, 1785–1825), Bass 22 (1994), 2, 566–625) and Jego 1597–1643), or discrete approximation. At critical = 1 / 2 1/2$ it shown that this coincides hyperbolic cosine Gaussian free field, closely related Liouville measure. This allows draw several conclusions elucidate connections between chaos, field For instance, Liouville-typical infinite multiplicity, relative contribution each overall thickness point being described Poisson–Dirichlet distribution parameter . Conversely, associated describes microscopic Along way, our proof reveals surprising exact integrability soup. also obtain some estimates continuous soups may be independent interest.