Sign up ×  Inspired by this question, I was curious about a
comment in this article:  In many situations, it can be easy to
apply Kolmogorov's zero-one law to show that some event has
probability 0 or 1, but surprisingly hard to determine which of
these two extreme values is the correct one.  Could someone
provide an example?  share|cite|improve this question I
especially like the way the conversation continues through
several posts. –  Ilya Nikokoshev Oct 27 '09 at 21:55  5 Answers
5  up vote 23 down vote accepted  There's a set of good examples
from percolation theory:  If you create a "random network" with
a certain probability p of edges between nodes (see article
above for precise definitions) then there is an infinite cluster
with probability either zero or one. But for a given value of p
it can be nontrivial to determine which.  share|cite|improve
this answer This is not a clear-cut. I think there could also be
values where p is between zero and one so I'm not sure the
Kolmogorov theorem applies –  Ily