Sur deux constructions de la gravité quantique de Liouville

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Sur deux constructions de la gravité quantique de Liouville
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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.
Classical physics Surface Random number Functional (mathematics) Weight Sheaf (mathematics) Insertion loss Sphere Random measure Frequency Latent heat Cross-correlation Insertion loss Lecture/Conference Well-formed formula Gravitation Matrix (mathematics) Summierbarkeit Compact space Link (knot theory) Measurement Sphere Well-formed formula Cross-correlation Function (mathematics) Gravitation Object (grammar) Volume
Geometry Point (geometry) Link (knot theory) Transformation (genetics) Automorphism Theory Measurement Local Group Frequency Insertion loss Modulform Algebra Maß <Mathematik> Fiber (mathematics) Link (knot theory) Theory of relativity Automorphism Moment (mathematics) Interior (topology) Infinity Transformation (genetics) Cartesian coordinate system Limit (category theory) Automorphism Plane (geometry) Computer animation Phase transition Volume Identical particles Family Resultant
Logical constant Randomization Group action Zeitdilatation Distribution (mathematics) Weight Correspondence (mathematics) Quantum fluctuation Sheaf (mathematics) Insertion loss Sphere Mereology Measurement Estimator Volume Plane (geometry) Insertion loss Dedekind cut Thermal fluctuations 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 Modulo (jargon) Sample (statistics) Bessel function Quadratic equation Mathematical singularity Volume Bounded variation Point (geometry) Slide rule Random number Free group Functional (mathematics) Conformal map Process (computing) Algebraic structure Modulform Translation (relic) Limit (category theory) Average Subgroup Equivalence relation Axonometric projection Rule of inference Random measure Local Group Frequency Lecture/Conference Average Quotient Reduction of order Modulform Spacetime Lie group Maß <Mathematik> Dependent and independent variables Focus (optics) Distribution (mathematics) Twin prime Surface Volume (thermodynamics) Group action Limit (category theory) Sphere Planar graph Plane (geometry) Formal power series Voting Computer animation Circle Einbettung <Mathematik> Social class Object (grammar) Family Körper <Algebra> Maß <Mathematik>
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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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