Moments of Partition Functions of 2d Gaussian Polymers in the Weak Disorder Regime-I

Let W N ( β ) = E 0 e ∑ n = 1 N β ω ( n , S n ) - N β 2 / 2 be the partition function of a two-dimensional directed polymer in a random environment, where ω ( i , x ) , i ∈ N , x ∈ Z 2 are i.i.d. standard normal and { S n } is the path of a random walk. With β = β N = β ^ π / log N and β ^ ∈ ( 0 , 1...

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