Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, May 29, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Luca Gugelmann

Sharp thresholds and hypergraph 2-colorability

A sharp threshold p0 for e.g. a monotone graph property A in the random graph G(n,p) is a function of n and A such that for any epsilon > 0 we have that for p < (1-epsilon)p0 the probability that A holds is asymptotically 0 while for (1+epsilon)p0 it is asymptotically 1. A threshold function which is not sharp is called coarse. Many interesting graph properties are conjectured to have sharp thresholds, however proving that this is the case (let alone determining p0 exactly) is pretty hard in general. In his PhD thesis Ehud Friedgut proved several results characterizing properties with coarse thresholds. These results then can be used to prove by contradiction that other thresholds must be sharp. In this talk I will give an overview of these results and present a nice proof by Friedgut and Alon showing that the threshold for 2-colorability of a k-uniform hypergraph (with k > 2) is sharp.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2025  2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login