Leírás
Turán emlékelőadás 2.
Abstract:
Consider a random graph in the Erdős-Rényi G(n,p) model. Given monotone graph properties like
P1= "G is connected"
P2= "G contains a hamiltonian cycle"
P3= "The vertices of G can be covered by vertex disjoint triangles"
P4= "In every 2-coloring of the edges of G there is a monochromatic triangle,"
we would like to understand
1) What is the critical probability?
2) How large is the threshold interval?
For the case of connectivity, Erdős and Rényi pioneered this study and answered these two questions. In the lecture I will discuss general theorems for these questions and connections with extremal combinatorics, isoperimetric inequalities and Fourier methods, starting with the Bollobás-Thomason theorem on the threshold intervals, results on sharp thresholds by Friedgut and others, and the recent proof by Park and Pham of the expectation threshold conjecture posed by Jeff Kahn and me.
Join Zoom Meeting
https://us06web.zoom.us/j/82746435489?pwd=aFdsYmFzeFlMZHZYQUtydE5nU1Z6dz09
Meeting ID: 827 4643 5489
Passcode: 820099