The martingale approach to disorder irrelevance for pinning models. (English) Zbl 1221.82058

Lacoin, Hubert

Electron. Commun. Probab. 15, 418-427 (2010).

Summary: We present a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent alpha in \((0,1/2)\). We also give a new upper bound for the contact fraction of the disordered model at criticality.

MSC:

82B44	Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K37	Processes in random environments
60K05	Renewal theory