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- W4385721436 abstract "Let $$W_N(beta ) = {mathrm E}_0left[ e^{ sum _{n=1}^N beta omega (n,S_n) - Nbeta ^2/2}right] $$ be the partition function of a two-dimensional directed polymer in a random environment, where $$omega (i,x), iin mathbb {N}, xin mathbb {Z}^2$$ are i.i.d. standard normal and $${S_n}$$ is the path of a random walk. With $$beta =beta _N={hat{beta }} sqrt{pi /log N}$$ and $${hat{beta }}in (0,1)$$ (the subcritical window), $$log W_N(beta _N)$$ is known to converge in distribution to a Gaussian law of mean $$-lambda ^2/2$$ and variance $$lambda ^2$$ , with $$lambda ^2=log (1/(1-{hat{beta }}^2))$$ (Caravenna et al. in Ann Appl Probab 27(5):3050–3112, 2017). We study in this paper the moments $${{mathbb {E}}}[W_N( beta _N)^q]$$ in the subcritical window, for $$q=O(sqrt{log N})$$ . The analysis is based on ruling out triple intersections." @default.
- W4385721436 created "2023-08-11" @default.
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- W4385721436 date "2023-08-10" @default.
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- W4385721436 title "Moments of Partition Functions of 2d Gaussian Polymers in the Weak Disorder Regime-I" @default.
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- W4385721436 doi "https://doi.org/10.1007/s00220-023-04799-2" @default.
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