Off-Criticality and the Massive Brownian Loop Soup

Abstract

We introduce a natural "massive" version of the Brownian loop soup of Lawler and Werner which displays conformal covariance and exponential decay. We show that this massive Brownian loop soup arises as the near-critical scaling limit of a random walk loop soup with killing and is related to the massive SLE(2) identified by Makarov and Smirnov as the near-critical scaling limit of a loop-erased random walk with killing. We conjecture that the massive Brownian loop soup describes the zero level lines of the massive Gaussian free field, and discuss possible relations to other models, such as Ising, in the off-critical regime.

V2: 23 pages, added result, revised presentation

References in corpus (3)

• 2D growth processes: SLE and Loewner chains
• Conformal radii for conformal loop ensembles
• Level Lines of Gaussian Free Field I: Zero-Boundary GFF

Cited by in corpus (1)

• Brownian Loops and Conformal Fields