Add to ORKGLarge deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application for a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky Theorem.
Let V be a topological space and B(V ) the Borel oe--field on V . A sequence of probability measures...
AbstractWe study the diameters of sections of convex bodies in RN determined by a random N×n matrix ...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, cont...
Abstract. With any given convex body we associate three numbers that exhibit, respectively, its devi...
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
This paper proves large deviation theorems for a general class of random vectors taking values in Rd...
AbstractSharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quan...
Let B be an unconditional convex body in R^n in the ell-position. Then for any small epsilon, and fo...
We consider the convex hull of a finite sample of i.i.d. points uniformly distributed in a convex bo...
Our goal is to write an extended version of the notes of a course given by Olivier Guédon at the Po...
We study the diameters of sections of convex bodies in RN de-termined by a random N × n matrix Γ, ei...
International audienceThe text summarizes the general results of large deviations for empirical mean...
This article gives estimates on the covering numbers and diameters of random proportional sections a...
deviation probabilities for the number of vertices of random polytopes in the ball
Let V be a topological space and B(V ) the Borel oe--field on V . A sequence of probability measures...
AbstractWe study the diameters of sections of convex bodies in RN determined by a random N×n matrix ...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, cont...
Abstract. With any given convex body we associate three numbers that exhibit, respectively, its devi...
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
This paper proves large deviation theorems for a general class of random vectors taking values in Rd...
AbstractSharpening work of the first two authors, for every proportion λ∈(0,1) we provide exact quan...
Let B be an unconditional convex body in R^n in the ell-position. Then for any small epsilon, and fo...
We consider the convex hull of a finite sample of i.i.d. points uniformly distributed in a convex bo...
Our goal is to write an extended version of the notes of a course given by Olivier Guédon at the Po...
We study the diameters of sections of convex bodies in RN de-termined by a random N × n matrix Γ, ei...
International audienceThe text summarizes the general results of large deviations for empirical mean...
This article gives estimates on the covering numbers and diameters of random proportional sections a...
deviation probabilities for the number of vertices of random polytopes in the ball
Let V be a topological space and B(V ) the Borel oe--field on V . A sequence of probability measures...
AbstractWe study the diameters of sections of convex bodies in RN determined by a random N×n matrix ...
Existence of nicely bounded sections of two symmetric convex bodies K and L implies that th...