Axiomatic quantum field theory | Sobolev spaces | Logarithms
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: where is the -norm of , with being standard Gaussian measure on Unlike classical Sobolev inequalities, Gross's log-Sobolev inequality does not have any dimension-dependent constant, which makes it applicable in the infinite-dimensional limit. In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f where is the entropy functional. (Wikipedia).
Hamza Fawzi: "Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "Sum-of-squares proofs of logarithmic Sobolev inequalities on finite Markov chains" Hamza Fawzi - University of Cambridge Abstract: Logarithmic Sobolev inequalities play an important role in understanding the mixing times
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Liangbing Luo (U Conn) -- Logarithmic Sobolev Inequalities on Non-isotropic Heisenberg Groups
A Heisenberg group is the simplest non-trivial example of a sub-Riemannian manifold. In this talk, we will discuss the dimension (in)dependence of the constants in logarithmic Sobolev inequalities on non-isotropic Heisenberg groups. In this setting, a natural Laplacian is not an elliptic b
From playlist Northeastern Probability Seminar 2020
Inequalities for Math Olympiad: Logarithm Mean Value Inequality(Part 2)
This is part 2 of the topic on Logarithm Inequality: A tighter bound is introduced for Log(x) function and from which we derive the log mean value inequality. We will show some example problems that use the log inequality in next few videos. Please Like, Share and Subscribe!
From playlist Inequalities for Math Olympiad Series
Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form)
This video explains how to determine the value of several numbers on a logarithmic scale scaled in logarithmic form. http://mathispower4u.com
From playlist Using the Definition of a Logarithm
Ángela Capel: "Modified logarithmic Sobolev inequality for quantum spin systems via approximate..."
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "The modified logarithmic Sobolev inequality for quantum spin systems via approximate tensorization" Ángela Capel - Technische Universität München Abstract: Given a uniform, frustration-free family of local Lindbladians d
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Melchior Wirth: "From Entropic Curvature Bounds to Logarithmic Sobolev Inequalities"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "From Entropic Curvature Bounds to Logarithmic Sobolev Inequalities" Melchior Wirth - Institute of Science and Technology Austria (IST Austria), Department of Mathematics and Computer Science Abstract: One central questio
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021
Roland Bauerschmidt: Log-Sobolev inequality for the continuum Sine-Gordon model
The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations. Abstract: We derive a multiscale generalisation of the Bakry–Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an
From playlist Workshop: Workshop: Singular SPDEs and Related Topics
Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A
Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Logarithmic Equations
Concentration of quantum states from quantum functional (...) - N. Datta - Workshop 2 - CEB T3 2017
Nilanjana Datta / 24.10.17 Concentration of quantum states from quantum functional and transportation cost inequalities Quantum functional inequalities (e.g. the logarithmic Sobolev- and Poincaré inequalities) have found widespread application in the study of the behavior of primitive q
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Log-Sobolev inequality for near critical Ising and continuum φ4 measures - Roland Bauerschmidt
Mathematical Physics Seminar Topic: Log-Sobolev inequality for near critical Ising and continuum φ4 measures Speaker: Roland Bauerschmidt Affiliation: University of Cambridge Date: February 23, 2022 I will present results on Glauber dynamics of Ising models and continuum φ4 measures.
From playlist Mathematics
Properties of Logarithms : Logarithms, Lesson 5
This tutorial shows how a logarithm containing a product in its argument can be written as a sum of two logarithms, and how a logarithms of a quotient can be written as a subtraction of two logarithms. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTk
From playlist All About Logarithms
Flows of vector fields: classical and modern - Camillo DeLellis
Analysis Seminar Topic: Flows of vector fields: classical and modern Speaker: Camillo DeLellis Affiliation: Faculty, School of Mathematics; IBM von Neumann Professor, School of Mathematics Date: April 13, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Max Fathi: Ricci curvature and functional inequalities for interacting particle systems
I will present a few results on entropic Ricci curvature bounds, with applications to interacting particle systems. The notion was introduced by M. Erbar and J. Maas and independently by A. Mielke. These curvature bounds can be used to prove functional inequalities, such as spectral gap bo
From playlist HIM Lectures: Follow-up Workshop to JTP "Optimal Transportation"
Isolating a logarithm and using the power rule to solve
👉 Learn how to solve logarithmic equations. Logarithmic equations are equations with logarithms in them. To solve a logarithmic equation, we first isolate the logarithm part of the equation. After we have isolated the logarithm part of the equation, we then get rid of the logarithm. This i
From playlist Solve Logarithmic Equations
Denis Serre - Tenseurs symétriques positifs à divergence nulle. Applications.
UMPA, ENS Lyon, Prix Jacques-Louis Lions 2017 Réalisation technique : Antoine Orlandi (GRICAD) | Tous droits réservés
From playlist Des mathématiciens primés par l'Académie des Sciences 2017
Claire Chainais-Hillairet: Nonlinear free energy diminishing schemes for convection-diffusion...
The aim of the talk is to introduce a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift-diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation relation. This relation i
From playlist Numerical Analysis and Scientific Computing