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Gaussian free field and Liouville quantum gravity
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Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in which the problem was reduced to the study of certain "random surfaces". He further made the tantalising suggestion that this theory could be explicitly solved. Recent breakthroughs from the last fifteen years have not only given a concrete mathematical basis for this theory but also verified some of its most striking predictions, as well as Polyakov's original vision. This theory, now known in the mathematics literature either as Liouville quantum gravity or Liouville conformal field theory, is based on a remarkable combination of ideas coming from different fields, above all probability and geometry. This book is intended to be an introduction to these developments assuming as few prerequisites as possible.
Forward citations
Cited by 6 Pith papers
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Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity
A random walk that reflects off the boundary at infinity yields new algorithmic constructions of the free uniform spanning forest and a conjectural embedding framework for supercritical Liouville quantum gravity.
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Sharp moment and upper tail asymptotics for the critical $2d$ Stochastic Heat Flow
The h-th moment of the critical 2d Stochastic Heat Flow mass is at least exp(exp(c h)), matching a 1999 prediction and exponentially improving the known lower bound.
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Liouville Brownian motion and quantum cones in dimension $d > 2$
For even d > 2, the paper derives the spectral dimension of Liouville Brownian motion, shows it depends on the point thickness, and constructs higher-dimensional quantum cones.
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Tail Profile of Bulk Gaussian Multiplicative Chaos Measures I: Bulk/Boundary Quotients
The (p,q)-moment of the bulk/boundary quotient of Gaussian multiplicative chaos is finite whenever p is below min(2/γ²+q/2, 4/γ²), and blows up at the 4/γ² boundary.
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A quadratic BSDE approach to normalization for the finite volume 2D sine-Gordon model in the finite ultraviolet regime
A quadratic backward stochastic differential equation is used to define and prove weak convergence of an ultraviolet-regulated 2D sine-Gordon measure that is absolutely continuous with respect to the Gaussian free fie...
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Quasisymmetric geometry of low-dimensional random spaces
Random fractals from Brownian motion, SLE, and CLE are almost surely not quasisymmetrically equivalent to canonical spaces such as line segments, rays, or round carpets.
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