Calculus of Variations and Geometric Measure Theory
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A. Berarducci - P. Majer - M. Novaga

Infinite paths and cliques in random graphs

created by novaga on 16 Sep 2008
modified on 10 Nov 2018


Published Paper

Inserted: 16 sep 2008
Last Updated: 10 nov 2018

Journal: Fund. Math.
Volume: 216
Pages: 163-191
Year: 2012


We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made.

The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.


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