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Abstract
The contributions of Lucio Russo to the mathematics of percolation and disordered
systems are outlined. The context of his work is explained, and its ongoing impact on
current work is described and amplified.
Dedicated in friendship to Lucio
Russo
Keywords
percolation, Ising model, Russo's formula, RSW inequality,
box crossing, approximate zero-one law, influence, sharp
threshold
Mathematical Subject Classification 2010
Primary: 60K35, 82B20
Milestones
Received: 17 April 2016
Accepted: 19 May 2016
Published: 17 December 2016
Communicated by Raffaele Esposito
