Vol. 4, No. 3-4, 2016

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ISSN: 2325-3444 (e-only)
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The work of Lucio Russo on percolation

Geoffrey R. Grimmett

Vol. 4 (2016), No. 3-4, 199–211
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
Authors
Geoffrey R. Grimmett
Statistical Laboratory, Centre for Mathematical Sciences
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom