I think that in particular Erez Lapid has done a nice job with these two slides
http://www.math.clemson.edu/~jimlb/ConferenceTalks/ColumbiaWorkshop2006/lapid1.pdf
http://www.math.clemson.edu/~jimlb/ConferenceTalks/ColumbiaWorkshop2006/lapid2.pdf
Have a look in particular on page 10 in the first slide session for Bernstein's prinicple, and a proof of it is on page 11. The second slides focus on the higher rank situation.
By the way, the whole side is great: http://www.math.clemson.edu/~jimlb/coursenotes.html