Dual Functions and Heat Expansions

Dual Functions and Heat Expansions1

Quasi-orthogonal expansions for functions in BMO

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

Cluster Expansions and Correlation Functions

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecký–Preiss criterion. Expressions and estimates for correlation functions are also presented. The results are applied to systems of interacting classical and quantum particles, and to a lattice polymer model. 2000 Math. Subj. Class. 82B0...

Cluster Expansions & Correlation Functions

Cluster expansions were introduced at the dawn of Statistical Mechanics for the study of high temperature gases of interacting particles. They constitute a powerful perturbative method that is suitable for geometrically large systems, such as encountered in Statistical Physics. Numerous articles have contributed to the subject; a list of relevant publications is [GK, Cam, Bry, KP, Pfi, Dob, BZ,...

Semi-classical trace formulas and heat expansions

There is a strong similarity between the expansions of the heat kernel as worked out by people in Riemannian geometry in the seventies (starting with the famous “Can one hear the shape of a drum” by Mark Kac [Kac], the Berger paper [Berger] and the Mc-Kean-Singer paper [McK-Si]) and the so-called semi-classical trace formulas developed by people in semi-classical analysis (starting with Helffer...