Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, November 13, 2008, 12:15 pm

**Duration**: This information is not available in the database

**Location**: CAB G51

**Speaker**: Dominik Scheder

Consider the infinite two-dimensional integer grid, i.e. the graph
with the grid points **Z**^{2}, and edges between any two
points of unit distance. Choose a random subgraph *G* by
including each edge of the grid with probability *p*,
independently of each other. The Harris-Kesten theorem states that
the probability that *G* contains an infinite connected
component is 0 for *p* ≤ 1/2 and 1 for *p* > 1/2. The
original proof is quite technical, but in 2006 the paper mentioned
below gives a short and beautiful proof of it.

Béla Bollobás and Oliver Riordan, *A Short Proof of the Harris-Kesten Theorem*,
Bull. London Math. Soc. v38. 470-484, 2006.

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