3 research outputs found
Random polytopes obtained by matrices with heavy tailed entries
Let be an random matrix with independent entries and
such that in each row entries are i.i.d. Assume also that the entries are
symmetric, have unit variances, and satisfy a small ball probabilistic estimate
uniformly. We investigate properties of the corresponding random polytope
in (the absolute convex hull of rows of
). In particular, we show that where depends only on parameters in small ball inequality. This
extends results of \cite{LPRT} and recent results of \cite{KKR}. This inclusion
is equivalent to so-called -quotient property and plays an important
role in compressive sensing (see \cite{KKR} and references therein).Comment: Last version, to appear in Communications in Contemporary Mathematic
Random polytopes obtained by matrices with heavy tailed entries
Let be an random matrix with independent entries and
such that in each row entries are i.i.d. Assume also that the entries are
symmetric, have unit variances, and satisfy a small ball probabilistic estimate
uniformly. We investigate properties of the corresponding random polytope
in (the absolute convex hull of rows of
). In particular, we show that where depends only on parameters in small ball inequality. This
extends results of \cite{LPRT} and recent results of \cite{KKR}. This inclusion
is equivalent to so-called -quotient property and plays an important
role in compressive sensing (see \cite{KKR} and references therein).Comment: Last version, to appear in Communications in Contemporary Mathematic