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Endpoint distribution of directed polymers in 1+1 dimensions
directed polymers Endpoint distribution Probability
2011/7/28
Abstract: We give an explicit formula for the joint density of the max and argmax of the Airy$_2$ process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint ...
Duality mapping and unbinding transitions of semiflexible and directed polymers
Duality mapping unbinding transitions of semiflexible directed polymers
2010/11/19
Directed polymers (strings) and semiflexible polymers (filaments) are one-dimensional objects governed by tension and bending energy, respectively.They undergo unbinding transitions in the presence of...
Asymmetric directed polymers in random environments
Directed polymers in random environment Directed polymers in Brownian environments
2010/12/14
The model of Brownian Percolation has been introduced as an approx-imation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuati...
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...