|
|||||
 |
|
|
|
|
|
|
Around two theorems
and a lemma by Lucio Russo
Itai Benjamini and Gil Kalai
Vol. 6 (2018), No. 2, 69–75
|
Abstract |
|
We describe two directions of study following early work of Lucio Russo. The first direction follows the famous Russo–Seymour–Welsh (RSW) theorem. We describe an RSW-type conjecture by the first author which, if true, would imply a coarse version of conformal invariance for critical planar percolation. The second direction is the study of “Russo’s lemma” and “Russo’s 0–1 law” for threshold behavior of Boolean functions. We mention results by Friedgut, Bourgain, and Hatami, and present a conjecture by Jeff Kahn and the second author, which may allow applications for finding critical probabilities. |
Keywords
percolation, Russo–Seymour–Welsh theorem, Russo's lemma,
Russo's 0$\mskip1mu$–1 law, conformal uniformization,
discrete isoperimetry
|
Mathematical Subject Classification 2010
Primary: 60K35, 05C80, 30F10, 68QXX, 82B43
|
Milestones
Received: 16 January 2017
Revised: 3 January 2018
Accepted: 4 February 2018
Published: 29 May 2018
Communicated by Raffaele Esposito
|
Authors |
| Itai Benjamini | |
| Department of Mathematics Weizmann Institute Rehovot Israel |
|
| Gil Kalai | |
| Einstein Institute of
Mathematics Hebrew University of Jerusalem Givat Ram Campus Jerusalem Israel |
|
