Séminaire du 6 octobre 03, Christoph Richard.

Limit distributions and scaling behaviour for models of planar polygons

We discuss how the Airy distribution arises as limit distribution in models of planar polygons, whose perimeter and area generating function (PAGF) satisfies a q-algebraic functional equation. We then construct a formal asymptotic expansion of the PAGF about its tricritical point by deriving differential equations for the expansion coefficients. We finally present a numerical analysis of the (unsolved) self-avoiding polygon model and the planar random loop boundary.