Can you feel the double jump?

Details Can you feel the double jump? Can you feel the double jump?

1994-01-15

arxiv.org/abs/math/9401211v1

Random Structures Algorithms 5 (1994), 191--204

Mathematics

Logic

Scientific paper

Paul Erd\H{o}s and Alfred Renyi considered the evolution of the random graph G(n,p) as p ``evolved'' from 0 to 1. At p=1/n a sudden and dramatic change takes place in G. When p=c/n with c<1 the random G consists of small components, the largest of size Theta(log n). But by p=c/n with c>1 many of the components have ``congealed'' into a ``giant component'' of size Theta (n). Erd\H{o}s and Renyi called this the double jump, the terms phase transition (from the analogy to percolation) and Big Bang have also been proferred. Now imagine an observer who can only see G through a logical fog. He may refer to graph theoretic properties A within a limited logical language. Will he be able to detect the double jump? The answer depends on the strength of the language. Our rough answer to this rough question is: the double jump is not detectible in the First Order Theory of Graphs but it is detectible in the Second Order Monadic Theory of Graphs.

Affiliated with

Also associated with

No associations

Rating

Can you feel the double jump? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Can you feel the double jump?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Can you feel the double jump? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-155652