Probabilistic inequalities

Gaussian isoperimetric inequality

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and , and later independently by , states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. (Wikipedia).

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Graph the Solution to a System of Inequalities. (Quadratic/Linear) Bounded

This video explains how to graph the solution to a system of inequalities with a quadratic inequality and a linear inequality. http://mathispower4u.com

From playlist Solving Systems of Linear Inequalities

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Steven Heilman - Variational Proofs of Isoperimetric Inequalities

Recorded 11 February 2022. Steven Heilman of the University of Southern California presents "Variational Proofs of Isoperimetric Inequalities" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: We will first survey some variational proofs of the Euclidean and

From playlist Workshop: Calculus of Variations in Probability and Geometry

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Joe Neeman: Gaussian isoperimetry and related topics I

The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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Joe Neeman: Gaussian isoperimetry and related topics II

The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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Solving and graphing a linear inequality

👉 Learn how to solve multi-step linear inequalities having no parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-ste

From playlist Solve and Graph Inequalities | Multi-Step Without Parenthesis

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Joe Neeman: Gaussian isoperimetry and related topics III

The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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The Difference Between a Linear Equation and Linear Inequality (Two Variables)

This video explains the difference between a linear equation and linear inequality in two variables.

From playlist Solving Linear Inequalities in Two Variables

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Ex 1: Solve a Linear Inequality Given Function Notation Using a Graph

Solving a linear inequality given using function notation by analyzing the graphs of two functions. http://mathispower4u.com

From playlist Linear Inequalities in One Variable Solving Linear Inequalities

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Colloquium MathAlp 2016 - Michel Ledoux

Isopérimétrie dans les espaces métriques mesurés Le problème isopérimétrique (à volume donné, minimiser la mesure de bord, et déterminer les ensembles extrémaux), remonte aux temps les plus anciens. Tout à la fois, il peut se formuler de façon générale dans un espace métrique mesuré, et d

From playlist Colloquiums MathAlp

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Solving a multi step inequality

👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l

From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis

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Yuansi Chen: Recent progress on the KLS conjecture

Kannan, Lovász and Simonovits (KLS) conjectured in 1995 that the Cheeger isoperimetric coefficient of any log-concave density is achieved by half-spaces up to a universal constant factor. This conjecture also implies other important conjectures such as Bourgain’s slicing conjecture (1986)

From playlist Workshop: High dimensional measures: geometric and probabilistic aspects

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How to determine the solution of a system of linear inequalities by graphing

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of inequalities by Graphing | Standard Form

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Ex 2: Solve a Linear Inequality Given Using Function Notation Using a Graph

Solving a linear inequality given using function notation by analyzing the graphs of two functions. http://mathispower4u.com

From playlist Linear Inequalities in One Variable Solving Linear Inequalities

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Find the feasible region by graphing 4 linear inequalities

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

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Solving and Graphing an inequality when the solution point is a decimal

👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l

From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis

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Higher order curvatures and isoperimetric inequalities - Yi Wang

Yi Wang Member, School of Mathematics October 1, 2014 More videos on http://video.ias.edu

From playlist Mathematics

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Bo'az Klartag - Convexity in High Dimensions II

November 4, 2022 This is the second talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional convex sets, a

From playlist Minerva Mini Course - Bo'az Klartag

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Bo'az Klartag - Convexity in High Dimensions V

December 2, 2022 This is the fifth and final talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional conve

From playlist Minerva Mini Course - Bo'az Klartag

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Bo'az Klartag - Convexity in High Dimensions IV

November 18, 2022 This is the fourth talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional convex sets,

From playlist Minerva Mini Course - Bo'az Klartag

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Solving an inequality with a parenthesis on both sides

👉 Learn how to solve multi-step linear inequalities having parenthesis. An inequality is a statement in which one value is not equal to the other value. An inequality is linear when the highest exponent in its variable(s) is 1. (i.e. there is no exponent in its variable(s)). A multi-step l

From playlist Solve and Graph Inequalities | Multi-Step With Parenthesis

Related pages

Concentration of measure | Borell–TIS inequality | Brownian motion | Half-space (geometry) | Semigroup | Euclidean space | Minkowski content | Gaussian measure