Classical Statistical Mechanics and Witten Laplacians

During the past decade, the analysis of correlations in (mathematical) classical statistical mechanics has drawn much on the spectral theory of a deformed Hodge Laplacian, which was introduced by Witten in 1983 in a differential geometrical context. The starting point of this analysis is a resolvent identity which is now often refered to as the "Helffer-Sjoestrand formula", bearing the name of the two analysts who established it about 1994-6. The lecture reviews this past and also current developments.