Work

Conformally Invariant Fields Out of Brownian Loop Soups

Year: 2026

Type: article

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

Source: Memoirs of the American Mathematical Society

DOI: 10.1090/memo/1641

Authors: Antoine Jego, Titus Lupu, Wei Qian