Construction of Liouville Brownian motion via Dirichlet form theory

Jiyong Shin

Statistics & Probability Letters, 2019, vol. 148, issue C, 128-132

Abstract: The Liouville Brownian motion which was introduced in Garban et al. (2016) is a natural diffusion process associated with a random metric in two dimensional Liouville quantum gravity. In this paper we construct the Liouville Brownian motion via Dirichlet form theory. By showing that the Liouville measure is smooth in the strict sense, the positive continuous additive functional (Ft)t≥0 of the Liouville measure in the strict sense w.r.t. the planar Brownian motion (Bt)t≥0 is obtained. Then the Liouville Brownian motion can be defined as a time changed process of the planar Brownian motion BFt−1.

Keywords: Dirichlet forms; Liouville Brownian motion; Gaussian free field; Gaussian multiplicative chaos; Revuz correspondence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.01.013

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