Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers

Abstract

The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing the summation over the entire spectrum of excited states the problem is reduced to the Fredholm determinant with the Airy kernel which is known to yield the Tracy-Widom distribution

5 pages

References in corpus (5)

• Free-energy distribution of the directed polymer at high temperature
• Exact scaling functions for one-dimensional stationary KPZ growth
• Correlation functions of the one-dimensional attractive Bose gas
• Optimal fluctuation approach to a directed polymer in a random medium
• Joint free energy distribution in the random directed polymer problem

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