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We consider a simple random walk of length N, denoted by (Si)i∈{1, …, N}, and we define (wi)i≥1 a sequence of centered i.i.d. random variables. For K∈ℕ we define ((γi−K, …, γiK))i≥1 an i.i.d sequence of random vectors. We set β∈ℝ, λ≥0 and h≥0, and transform the measure on the set of random walk trajectories with the hamiltonian λ∑i=1N(wi+h)sign(Si)+β∑j=−KK∑i=1Nγij1{Si=j}. This transformed path measure describes an hydrophobic(philic) copolymer interacting with a layer of width 2K around an interface...
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