Sur deux constructions de la gravité quantique de Liouville

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Title
Sur deux constructions de la gravité quantique de Liouville
Title of Series
Part Number
7
Number of Parts
17
Author
Huang, Yichao
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Institut des Hautes Études Scientifiques (IHÉS)
Release Date
2016
Language
English

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Subject Area
Abstract
We will try to briefly review two recent mathematical constructions of some random measures defined on the Riemann sphere. These objects are motivated by a rigorous description of the Liouville Quantum Gravity (here on the sphere). We will try to compare these two constructions and relate several key elements that appear naturally in both approaches. If time permits, we can also discuss the advantage of each approach. Joint work with Juhan Aru and Xin Sun.
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Classical physics Surface Random number Sheaf (mathematics) Volume (thermodynamics) Insertion loss Sphere Random measure Summation Frequency Latent heat Cross-correlation Matrix (mathematics) Insertion loss Lecture/Conference Well-formed formula Gravitation Compact space Link (knot theory) Weight Sphere Measurement Functional (mathematics) Well-formed formula Cross-correlation Function (mathematics) Gravitation Object (grammar)
Geometry Point (geometry) Link (knot theory) Transformation (genetics) Volume (thermodynamics) Automorphism Theory Local Group Measurement Frequency Insertion loss Fiber (mathematics) Link (knot theory) Theory of relativity Automorphism Moment (mathematics) Interior (topology) Infinity Transformation (genetics) Limit (category theory) Cartesian coordinate system Bilinear form Automorphism Plane (geometry) Computer animation Phase transition Units of measurement Family Identical particles Resultant
Logical constant Spacetime Randomization Group action Zeitdilatation Correspondence (mathematics) Quantum fluctuation Thermal fluctuations Embedding Sheaf (mathematics) Insertion loss Sphere Mereology Volume Plane (geometry) Insertion loss Dedekind cut Hausdorff dimension Physical law Circle Vertex (graph theory) Noise Bounded variation Family Injektivität Fisher's exact test Theory of relativity Process (computing) Point (geometry) Moment (mathematics) Sampling (statistics) Iterated function system Thermal expansion Mereology Measurement Bilinear form Functional (mathematics) Modulo (jargon) Sample (statistics) Bessel function Quadratic equation Mathematical singularity Bounded variation Point (geometry) Slide rule Random number Free group Conformal map Process (computing) Distribution (mathematics) Algebraic structure Modulform Volume (thermodynamics) Translation (relic) Limit (category theory) Average Subgroup Equivalence relation Axonometric projection Rule of inference Random measure Local Group Measurement Frequency Lecture/Conference Average Quotient Reduction of order Lie group Units of measurement Focus (optics) Twin prime Distribution (mathematics) Surface Volume (thermodynamics) Weight Group action Limit (category theory) Sphere Estimator Planar graph Plane (geometry) Formal power series Voting Computer animation Circle Field (mathematics) Dependent and independent variables Social class Object (grammar) Units of measurement Family
Spacetime Group action Randomization Zeitdilatation Sphere Mereology Cartesian coordinate system Explosion Summation Casting (performing arts) Physical law Noise Arc (geometry) Point (geometry) Infinity Mereology Measurement Flow separation Modulo (jargon) Proof theory Sample (statistics) Bessel function Theorem Point (geometry) Random number Free group Conformal map Volume (thermodynamics) Equivalence relation Axonometric projection Metric tensor Measurement Frequency Operator (mathematics) Boundary value problem Normal (geometry) Shift operator Distribution (mathematics) State of matter Weight Sphere Approximation Plane (geometry) Calculation Summation Computer animation Circle Social class Units of measurement
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school .period construction this is a very interesting construction in the sense that they use sometimes of encoding of of your service you can construct surface by using a basso process somewhere so the idea behind this is that if you take a function that is the final complex plane you can decompose into 2 parts the 1st I would tell you just the average of dysfunction on initially circles the valley averaged over the function of a functional each 1 in circles you don't know much about its function if you want to know entirely the function you must ask legislation but dysfunction on everyone is surfaced so if it combines 2 parts you will get your function or distribution now the point of this construction is that you can sample actually reduce Greece parts in the independent way and we can give explicit constructions explicit ways to sample the now I would not talk about the fluctuation Papas has given by some actress matter but is not very the difficulty and outslugged about this part the average office and with the wife of the construction is invariant under section so what you do well this is a little too hard to read perhaps the 1st meal but when you do we use the latter Basso's 1st and it's taken a lot of these specimens version it looked like something like this is so are you process like that you like something that we call them to sign a drifting running motion it was my brother motion that was once year and wanted now didn't Didier the rule is that we were Paris twice this so that it will look like a brand but if you think about it I can translate my picture that constant and it does not change the fact that has put variations so actually we do this you're defining a process that is invariant underneath on translation so if you if you take this fisher back to sphere the whole plane you're defining an object that is invariant under this because the longer does not depend on the special so
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