Strong and Weak Disorder for Lévy Directed Polymers in Random Environment

Abstract

We consider Lévy directed polymers in the Poisson random environment. We give conditions for strong or weak disorder in terms of the Lévy exponent of symmetric Lévy process.

Keywords:

• Random environment
• Strong disorder
• Symmetric Lévy process
• Symmetric α-stable process
• Weak disorder

Mathematics Subject Classification:

• Primary 60K37
• Secondary 60J75

We thank Professor Masayoshi Takeda for his helpful advice and comments. We also thank an anonymous referee for a careful reading of this article and helpful comments.