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- W4200629547 abstract "Let $W_N(beta) = mathrm{E}_0left[e^{ sum_{n=1}^N betaomega(n,S_n) - Nbeta^2/2}right]$ be the partition function of a two-dimensional directed polymer in a random environment, where $omega(i,x), iin mathbb{Z}_+, xin mathbb{Z}^2$ are i.i.d. standard normal and ${S_n}$ is the path of a random walk. With $beta=beta_N=hatbeta sqrt{pi/log N}$ and $hat betain (0,1)$ (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 $lambda^2=log big(1/(1-hatbeta^2big)$ (Caravenna, Sun, Zygouras, Ann. Appl. Probab. (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.
- W4200629547 created "2021-12-31" @default.
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- W4200629547 date "2021-12-07" @default.
- W4200629547 modified "2023-09-29" @default.
- W4200629547 title "Moments of partition functions of 2D Gaussian polymers in the weak disorder regime" @default.
- W4200629547 hasPublicationYear "2021" @default.
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