Modul:   MAT971  Seminar über stochastische Prozesse

On the phase transition of self-attracting polymers under stretching

Vortrag von Dr. Yvan Velenik

Datum: 17.04.13  Zeit: 17.15 - 19.00  Raum: Y27H25

We consider a general class of self-attracting polymer models under stretching (or, equivalently, self-attracting random walks with drift).

It is well-known that such models undergo a phase transition as the intensity of the stretching force increases: at weak intensity, the polymer has a vanishing macroscopic extension (collapsed phase), while above a critical intensity, the polymer acquires a nonzero macroscopic extension (stretched phase).

In dimensions 2 and above, this phase transition turns out to be always of first order, the macroscopic extension of the polymer, as a function of the intensity of the stretching force, being discontinuous at the transition. Moreover, at criticality the polymer still has a nonvanishing macroscopic extension, with Gaussian fluctuations.

The talk is based on a joint work with Dmitry Ioffe [Self-Attractive Random Walks: The Case of Critical Drifts, Commun. Math. Phys. 313, 209-235 (2012)].