Conformally Invariant Fields Out of Brownian Loop Soups
Abstract
Consider a Brownian loop soup L D θ \mathcal {L}_D^\theta with subcritical intensity θ ∈ ( 0 , 1 / 2 ] \theta \in (0,1/2] in some 2D bounded simply connected domain D D . We define and study the properties of a conformally invariant field h θ h_\theta naturally associated to L D θ \mathcal {L}_D^\theta . Informally, this field is a signed version of the local time of L D θ \mathcal {L}_D^\theta to the power 1 − θ 1-\theta . When θ = 1 / 2 \theta = 1/2 , h θ h_\theta is a Gaussian free field (GFF) in D D . Our construction of h θ h_\theta relies on the multiplicative chaos M
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Mathematical Dynamics and Fractals
Plant Water Relations and Carbon Dynamics
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 322
- Issue
- 1641
- Publication date
- 14 August 2026
- Language
- EN