In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the...

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov, and later independently by Christer Borell, states...

estimators Gaussian correlation inequality Gaussian isoperimetric inequality Gibbs's inequality Hoeffding's inequality Hoeffding's lemma Jensen's inequality Khintchine...

SDE which has a weak solution but no strong solution. The Gaussian isoperimetric inequality (proved by Vladimir Sudakov and Tsirelson, and independently...

Gauss–Markov theorem Gaussian copula Gaussian measure Gaussian correlation inequality Gaussian isoperimetric inequality Gauss's inequality Gauss-Helmert model...

Bobkov's inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The...

Gauss's inequality Gauss–Kuzmin distribution Gauss–Markov process Gauss–Markov theorem Gauss–Newton algorithm Gaussian function Gaussian isoperimetric inequality...

volume ratios and isoperimetric quotients for convex sets in and. There is also a geometric version of the more general inequality in which the maps B...

(}{\frac {-u^{2}}{2\sigma _{T}^{2}}}{\bigg )}} . Gaussian isoperimetric inequality "Gaussian Inequalities". Random Fields and Geometry. Springer Monographs...

thermodynamics. Borell–TIS inequality Gaussian isoperimetric inequality McDiarmid's inequality Talagrand's concentration inequality Asymptotic equipartition...

The Sobolev inequality is equivalent to the isoperimetric inequality (in any dimension), with the same best constants. Wirtinger's inequality also generalizes...

However, the inequality goes in the opposite direction. Thus, Pu's inequality can be thought of as an "opposite" isoperimetric inequality. Filling area...

process Gauss–Markov process Gaussian process Gaussian random field Gaussian isoperimetric inequality Large deviations of Gaussian random functions Girsanov's...

m-dimensional Hausdorff measure of A. Gaussian isoperimetric inequality Geometric measure theory Isoperimetric inequality in higher dimensions Minkowski–Bouligand...

of the length. Mikhail Gromov once voiced the opinion that the isoperimetric inequality was known already to the Ancient Greeks. The mythological tale...

matrix. The Fisher information matrix plays a role in an inequality like the isoperimetric inequality. Of all probability distributions with a given entropy...

S2CID 53244523. Dodziuk, Jozef (1984), "Difference equations, isoperimetric inequality and transience of certain random walks", Trans. Amer. Math. Soc...

used the invariance principle in conjunction with an isoperimetric theorem of Borell in Gaussian space; since then more direct proofs were devised. Majority...

Codá Marques and André Neves. Isoperimetric inequalities. In 1939 Schmidt proved that the classical isoperimetric inequality for curves in the Euclidean...

covariance matrices Fractional Brownian motion Gaussian isoperimetric inequality Gaussian measure / anl Gaussian random field Gauss–Markov process / Mar Integration...

bounded Gaussian processes in very general settings, and also new methods to bound stochastic processes. He discovered new aspects of the isoperimetric and...

sphere is the one having the greatest volume. It follows from isoperimetric inequality. These properties define the sphere uniquely and can be seen in...

important connections to isoperimetric inequalities, see more here, functional inequalities such as Sobolev and Poincaré inequalities and properties of solutions...

This inequality can be thought of as analogous to Bonnesen's inequality with isoperimetric defect, a strengthening of the isoperimetric inequality. A number...

surface energy, to Gaussian measure of surfaces, and to Euclidean spaces of any dimension. According to the isoperimetric inequality, the minimum-perimeter...

The curve-shortening flow can be used to prove an isoperimetric inequality for surfaces whose Gaussian curvature is a non-increasing function of the distance...

supervision of Xavier Fernique. He has done important research on the isoperimetric inequality in analysis and probability theory. In 2010 he received the Servant...

particularly in high dimensions. Basic examples include "isomorphic isoperimetric inequalities" which are closely linked to the concentration of measure phenomenon...

conditional assumptions. Around the same time, a similar inequality was obtained by isoperimetric methods by Mikhael Gromov, although his result is weaker...

Grushko theorem (group theory) Higman's embedding theorem (group theory) Isoperimetric gap (geometric group theory, metric geometry) Jordan–Hölder theorem...