## An almost sure CLT for stretched polymers.(English)Zbl 1286.60026

The authors consider diffusive behaviour in $${\mathbb Z}^{d+1}$$, $$d\geq 3$$, for the related models of stretched polymers. A stretched path $$\gamma$$ can be any nearest-neighbour path on $${\mathbb Z}^{d+1}.$$ The disorder is modeled by a collection $$\{V(x)\}_{x\in {\mathbb Z}^{d+1}}$$ of i.i.d. non-negative random variables. Each visit of the path to a vertex $$x$$ exerts the price $$\exp(-\beta V(x))$$, $$\beta>0$$. One (of two) way of introduction of the stretch is that the path $$\gamma$$ has a fixed length, but it is subject to a drift, which can be interpreted physically as the effect of a force acting on the polymer’s free end. In the paper, an almost-sure central limit theorem is established for the endpoint of the fixed-length version of the model of stretched polymers with non-zero drifts, also at sufficiently high temperatures and in all dimensions $$d+1\geq 4$$.

### MSC:

 60F05 Central limit and other weak theorems 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics 82D60 Statistical mechanics of polymers
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