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We explore the geometric meaning of the so-called zeta-regularized determinant of the Laplace-Beltrami operator on a compact surface, with or without boundary.
Liouville quantum gravity with matter central charge in ( 1 , 25 ) (1,25) : a probabilistic approach
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E. Gwynne and J. Miller · 1905
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E. Gwynne and J. Miller · 1905
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E. D’Hoker and D. H. Phong · 1986
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M. E. Cates · 1988
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Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice
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J. Distler and H. Kawai · 1989
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Stochastic calculus in manifolds
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A naive matrix-model approach to 2D quantum gravity coupled to matter of arbitrary central charge
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S. Catterall, J. Kogut, and R. Renken · 1992
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N. Berestycki · 2015
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Introduction to the gaussian free field and liouville quantum gravity
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An almost sure KPZ relation for SLE and Brownian motion
E. Gwynne, N. Holden, and J. Miller · 2015
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Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric
J. Miller and S. Sheffield · 2015
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Liouville Brownian motion at criticality
R. Rhodes and V. Vargas · 2015
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R. Kenyon · 2000
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The Mellin transform and other useful analytic techniques, appendix to E. Zeidler
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Polyakov’s formulation of 2 d 2d bosonic string theory
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Imaginary geometry I: interacting SLEs
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On Gaussian multiplicative chaos
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Two perspectives of the 2D unit area quantum sphere and their equivalence
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Gaussian multiplicative chaos through the lens of the 2D Gaussian free field
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Regularized limit of determinants for discrete tori
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Equivalent descriptions of the Loewner energy
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Liouville quantum gravity spheres as matings of finite-diameter trees
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The energy of a deterministic Loewner chain: reversibility and interpretation via SLE 0 + {\rm SLE}_{0+}
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Lecture notes on the gaussian free field
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