Quantum gravity and inventory accumulation

DOI10.1214/15-AOP1061zbMath1359.60120arXiv1108.2241OpenAlexW2963346680MaRDI QIDQ504248

Scott Sheffield

Publication date: 13 January 2017

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2241

zbMATH Keywords

random walksBrownian motionscaling limitSchramm-Loewner evolutionplanar mapLiouville quantum gravitycontinuum random treeFK random cluster modelinventory accumulation

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stopping times; optimal stopping problems; gambling theory (60G40) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (50)

Imaginary geometry. I: Interacting SLEs ⋮ The perimeter cascade in critical Boltzmann quadrangulations decorated by an \(O(n)\) loop model ⋮ Counting coloured planar maps: differential equations ⋮ Limits of the boundary of random planar maps ⋮ A linearized circle packing algorithm ⋮ Chordal \(\mathrm{SLE}_6\) explorations of a quantum disk ⋮ An axiomatic characterization of the Brownian map ⋮ Connection probabilities for conformal loop ensembles ⋮ Critical exponents on Fortuin-Kasteleyn weighted planar maps ⋮ An almost sure KPZ relation for SLE and Brownian motion ⋮ Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for \(\kappa>8\) ⋮ Simple peeling of planar maps with application to site percolation ⋮ Imaginary geometry. IV: Interior rays, whole-plane reversibility, and space-filling trees ⋮ Hamiltonian cycles on bicolored random planar maps ⋮ Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ Uniqueness of the critical and supercritical Liouville quantum gravity metrics ⋮ Uniqueness of the infinite noodle ⋮ Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\) ⋮ Brownian half‐plane excursion and critical Liouville quantum gravity ⋮ Conformal welding of quantum disks ⋮ Nesting statistics in the \(O(n)\) loop model on random planar maps ⋮ Integrability of SLE via conformal welding of random surfaces ⋮ What is a random surface? ⋮ Anomalous diffusion of random walk on random planar maps ⋮ Brownian motion correlation in the peanosphere for \(\kappa>8\) ⋮ Critical behaviour of spanning forests on random planar graphs ⋮ Existence and uniqueness of the Liouville quantum gravity metric for \(\gamma \in (0, 2)\) ⋮ Local convergence of large random triangulations coupled with an Ising model ⋮ CLE PERCOLATIONS ⋮ A distance exponent for Liouville quantum gravity ⋮ The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds ⋮ Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity ⋮ Induced graphs of uniform spanning forests ⋮ Inventory Accumulation with $k$ Products ⋮ Liouville quantum gravity and the Brownian map. I: The \(\text{QLE}(8/3,0)\) metric ⋮ Random walk on random planar maps: spectral dimension, resistance and displacement ⋮ External diffusion-limited aggregation on a spanning-tree-weighted random planar map ⋮ The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity ⋮ SLE as a mating of trees in Euclidean geometry ⋮ Liouville dynamical percolation ⋮ Liouville quantum gravity surfaces with boundary as matings of trees ⋮ Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense ⋮ The generating function of planar Eulerian orientations ⋮ Tree-decorated planar maps ⋮ Harmonic functions on mated-CRT maps ⋮ UNIQUENESS OF THE WELDING PROBLEM FOR SLE AND LIOUVILLE QUANTUM GRAVITY ⋮ Metric gluing of Brownian and \(\sqrt{8/3}\)-Liouville quantum gravity surfaces ⋮ A mating-of-trees approach for graph distances in random planar maps ⋮ Liouville quantum gravity spheres as matings of finite-diameter trees ⋮ Ribbon tilings and multidimensional height functions

This page was built for publication: Quantum gravity and inventory accumulation