Schramm Loewner Evolution and Liouville Quantum Gravity
Mathematical Physics
2015-05-20 v1 Statistical Mechanics
Complex Variables
math.MP
Probability
Abstract
We conformally weld (via "quantum zipping") two boundary arcs of a Liouville quantum gravity random surface to generate a random curve called the Schramm-Loewner evolution (SLE). We develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under welding via SLE martingales. As an application, we construct the natural quantum length and boundary intersection measures on the SLE curve itself.
Cite
@article{arxiv.1012.4800,
title = {Schramm Loewner Evolution and Liouville Quantum Gravity},
author = {Bertrand Duplantier and Scott Sheffield},
journal= {arXiv preprint arXiv:1012.4800},
year = {2015}
}
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