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Stochastik AG

Nov 21
21-11-2019 14:15 Uhr bis 16:00 Uhr
H13

Nicolas Petrelis (Nantes)

Titel: Phase diagram and scaling limits of the 2-dimensional IPDSAW (Interacting Partially-Directed Self-Avoiding Walk)

Abstract:
We will describe and study the Interacting Partially-Directed Self-Avoiding Walk (IPDSAW): a model initially introduced in 1968 by Zwanzig and Lauritzen to investigate the collapse transition of an homopolymer dipped in a poor solvent. We will begin by displaying a new probabilistic representation of the partition function (based on an auxiliary random walk) which relates some geometric features of IPDSAW trajectories to that of a particular random walk conditioned on enclosing a prescribed geometric area. This method allowed us to push the mathematical understanding of IPDSAW some steps further in the last years. We will illustrate this new family of results by providing a sharp geometric description of a typical configuration of IPDSAW in each regime (i.e., collapsed, extended and critical).