Spectral dimension of Liouville quantum gravity

DOI10.1007/s00023-013-0308-yzbMath1305.83036arXiv1305.0154OpenAlexW3105643191WikidataQ125972574 ScholiaQ125972574MaRDI QIDQ481791

Vincent Vargas, Rémi Rhodes

Publication date: 15 December 2014

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0154

Mathematics Subject Classification ID

Applications of statistics to physics (62P35) Quantization of the gravitational field (83C45) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Analogues of general relativity in lower dimensions (83C80)

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Liouville Brownian motion and thick points of the Gaussian free field ⋮ Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions ⋮ Random walks on mated-CRT planar maps and Liouville Brownian motion ⋮ Gaussian multiplicative chaos and applications: a review ⋮ Measure-geometric Laplacians for partially atomic measures ⋮ Liouville Brownian motion at criticality ⋮ A distance exponent for Liouville quantum gravity ⋮ The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds ⋮ Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation ⋮ Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity ⋮ Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field ⋮ Random walk on random planar maps: spectral dimension, resistance and displacement ⋮ KPZ formula derived from Liouville heat kernel ⋮ Heat kernel for Liouville Brownian motion and Liouville graph distance ⋮ Liouville quantum gravity on the Riemann sphere

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