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A note on the asymptotics of the free energy of $1+1$ dimensional directed polymers in random environment at high temperature
Makoto Nakashima · 2025-03-26 · via math.PR updates on arXiv.org

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 $β\to 0$ under the assumption that random environment satisfies a certain concentration inequality in [Nak19], \[\lim_{β\to0}\frac{1}{β^4}F(β)=-\frac{1}{6}. \] In this paper, we obtain the same asymptotics without using the concentration inequality.

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