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Majorizing multiplicative cascades for directed polymers in random media
Directed polymers random environment strong disorder generalized multiplicative cascades
2009/6/12
In this note we give upper bounds for the free energy of discrete directed polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theo...
Strong disorder implies strong localization for directed polymers in a random environment
Directed polymers Random environment strong disorder localization parabolic Anderson
2009/6/12
In this note we show that in any dimension d, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymersin arandom envi...
A Condition for Weak Disorder for Directed Polymers in Random Environment
Directed polymer in random environment weak disorder size-biasing
2009/4/28
We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representation of the si...