Mathematically proved limits on marathon times

What is the fastest theoretical time that a human can run a marathon? According to Dutch mathematician John Einmahl of Germany's Tilberg University, Paul Tergat could improve his world record time of 2:04:55 by 49 seconds. Women marathoners could take as much as 8:50 off Paula Radcliffe's 2:15:25 world record. Sprinters, apparently, could do even better from a percentage perspective.

(Paul Tergat sets the world marathon record in Berlin, Germany in 2003 -
don't tell him he could have gone 49 seconds faster!)

It's all part of the mathematical study of "extreme values" that helps determine upper limits. A quote from the story:

"For a lot of athletes it is probably depressing when they are confronted with our extreme values," Einmahl told the German news agency dpa. "But this is a very serious study - the extreme theory as a part of mathematics and statistics is an accepted science."

It's all math, so there is certainly the chance of a breakout performance. I wonder what the 100-mile limit would be? Perhaps this will be one of Professor Einmahl's graduates thesis.

SD

[Thanks to The Final Sprint for pointing me to this story]