A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature

Makoto Nakashima

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arXiv · 2503.20192

A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature

Makoto Nakashima

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Abstract

The author gave the sharp asymptotic behavior of the free energy of $1+1$ dimensional directed polymers in random environment(DPRE) as the inverse temperature $\beta\to 0$ under the assumption that random environment satisfies a certain concentration inequality in [Nak19], \[\lim_{\beta\to0}\frac{1}{\beta^4}F(\beta)=-\frac{1}{6}. \] In this paper, we obtain the same asymptotics without using the concentration inequality.

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Makoto Nakashima. 2025-03-26. A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature. https://arxiv.org/abs/2503.20192

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