Producción CyT
Artículo
Autoría
GALICER, DANIEL ERIC
;
Damián Pinasco
;
Mariano Merzbacher
;
Alexander Litvak
Fecha
2023
Editorial y Lugar de Edición
ACADEMIC PRESS INC ELSEVIER SCIENCE
Revista
JOURNAL OF FUNCTIONAL ANALYSIS
ACADEMIC PRESS INC ELSEVIER SCIENCE
Resumen
Información suministrada por el agente en
SIGEVA
We study the volume ratio between emph{projections} of two convex bodies.Given a high-dimensional convex body $K$ we show that there is another convex body$L$ such that the volume ratio between any two projections of fixed rank of the bodies$K$ and $L$ is large. Namely, we prove that for every $1leq kleq n$ and foreach convex body $Ksubset R^n$there is a centrally symmetric body $L subset R^n$ such that for any two projections $P, Q: R^n o R^n$ of rank $k$ one has$$ r(PK, QL) geq c , minleft{ra...
We study the volume ratio between emph{projections} of two convex bodies.Given a high-dimensional convex body $K$ we show that there is another convex body$L$ such that the volume ratio between any two projections of fixed rank of the bodies$K$ and $L$ is large. Namely, we prove that for every $1leq kleq n$ and foreach convex body $Ksubset R^n$there is a centrally symmetric body $L subset R^n$ such that for any two projections $P, Q: R^n o R^n$ of rank $k$ one has$$ r(PK, QL) geq c , minleft{rac{ k}{ sqrt{n}} , sqrt{rac{1}{log log log(rac{nlog(n)}{k})}}, , rac{sqrt{k}}{sqrt{log(rac{nlog(n)}{k})}}},$$ where $c>0$ is an absolute constant.This general lower bound is sharp (up to logarithmic factors)in the regime $kgeq n^{2/3}$.
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Palabras Clave
Projections of convex bodiesVolume ratioConvex BodiesRandom Polytopes