Random surfaces and Liouville quantum gravity
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Gwynne, Ewain
Abstract
Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in the same sense that Brownian motion is the canonical model of a random path. LQG surfaces are the continuum limits of discrete random surfaces called random planar maps. In this expository article, we discuss the definition of random planar maps and LQG, the sense in which random planar maps converge to LQG, and the motivations for studying these objects. We also mention several open problems. We do not assume any background knowledge beyond that of a second-year mathematics graduate student.
Description
Keywords
4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Notices of the American Mathematical Society
Conference Name
Journal ISSN
0002-9920
1088-9477
1088-9477
Volume Title
67
Publisher
American Mathematical Society
Publisher DOI
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All rights reserved