The quenched limiting distributions of a charged-polymer model in one and two dimensions
Résumé
Let $(q_i)_{i\geq 1}$ be a random field of i.i.d. random variables, which is called the random charges, and a random walk $(S_n)_{n \in N}$ evolving in $Z^d$, independent of the charges. In this paper we consider the limit distributions of the Hamiltonian $K=(K_n)_{n \geq 2}$ defined as $K_n := \sum_{i=2}^n \sum_{j=1}^{i-1} q_i q_j 1_{S_i=S_j}$ under the conditional law given $q$ in dimension d=1 and 2.
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