Valentine Zuber (dir.), La liberté religieuse

Notion de liberté en statistique mathématique

New Scaling of Itzykson-zuber Integrals

ABSTRACT. We study asymptotics of the Itzykson-Zuber integrals in the scaling when one of the matrices has a small rank compared to the full rank. We show that the result is basically the same as in the case when one of the matrices has a fixed rank. In this way we extend the recent results of Guionnet and Maı̈da who showed that for a latter scaling the Itzykson-Zuber integral is given in terms ...

Pair Correlator in the Itzykson-zuber Integral

where ∆(φ) ≡ ∏N i<j(φi − φj) ≡ Φ1...N , P are arbitrary permutations of N elements and VN is the volume of the unitary group. This result was first obtained independently in [1] and [2]. It can be also interpreted in terms of the orbit integrals on the lines of [3] and in terms of the Duistermaat-Heckman (DH) theory (see [4]). In this letter the expression for the first non-trivial generalizati...

The Cappelli–Itzykson–Zuber A–D–E Classification

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed – in hindsight the reason is that their argument ignored most of the rich structure present. We give ...

James W. Valentine

Jim Valentine went to college on the GI Bill (a WWII veterans privilege) and has been there ever since; at present he is Professor of Integrative Biology, Emeritus, at UC Berkeley. His early research was on what is now called macroecology, working with fossil marine faunas, leading to a book, Evolutionary Paleoecology of the Marine Biosphere. Those studies continue today, chiefly with colleague...