On the free energy of a directed polymer in a Brownian environment
John Moriarty, Neil O'Connell
TL;DR
This paper proves a conjectured formula for the free energy density of a directed polymer in a 1+1 dimensional Brownian environment, advancing understanding of stochastic polymer models.
Contribution
It provides a rigorous proof of a previously conjectured formula for the free energy density in a specific stochastic environment.
Findings
Confirmed the conjectured formula for free energy density.
Enhanced theoretical understanding of directed polymers in Brownian environments.
Established a foundation for further analytical studies in stochastic polymer models.
Abstract
We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Random Matrices and Applications