The crossing probability for directed polymers in random media
arXiv:1505.04802 · doi:10.1103/PhysRevE.92.040102
Abstract
We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain analytical expressions for the first few moments of this probability, and compare them to a numerical simulation of a discrete model at high-temperature. From these observations, several large time properties of the non-crossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed.
5 pages + 16 pages of supplemental material (Minor misprints corrected, references added)
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Cited by in corpus (8)
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- Intermediate disorder limits for multi-layer semi-discrete directed polymers
- Real-time correlators in chaotic quantum many-body systems
- Crossing probability for directed polymers in random media: exact tail of the distribution
- Mutually avoiding paths in random media and largests eigenvalues of random matrices
- Distribution of Brownian coincidences
- A stationary model of non-intersecting directed polymers