problem: the result completes the picture about the properties of $l_1$ with large $p$ and $n$ and, in a sense, closes Theorem \[ThJ\]. But is it interesting from a statistical standpoint?

The situation $p\gg n$ is indeed a fairly common one in modern statistics. Microarray data are a prototypical example: currently they usually have $p$ of the order of a few thousands and $n$ of the order of a few tens. One encounters $p\gg n$ or $n\gg p$ in many other instances: data collection mechanisms are now effective enough so as to, for example, collect and retain thousands of piece of information for millions of customers (transactional data), or millions of pieces of information for thousands of stocks (tick-by-tick data in Finance). Analyzing these very high dimensional datasets raises new challenges and is at the center of recent statistical work, both applied and theoretical.

Microarray analysis in particular is a very active field, and has contributed a flurry of activity in non classical situations (very high dimensional data), raising theoretical questions and sometimes revisiting classical techniques or results. As illustrated for instance in @wrr, PCA or PCA-related methods are used for various tasks in the microarray context, from traditional dimensionality 