In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy =∑ 1 of the polymer { , …, } equipped with random electrical charges { , …, }. Our approach is based on comparison of the moments between and the self-intersection local time =∑1 run by the -dimensional...
We study functionals of the form = ⋯ | ( )+⋯+ ( )| d ⋯ d , where (), …, () are i.i.d. -dimensional symmetric stable processes of index 0<≤2. We obtain results about the large deviations and laws of the iterated logarithm for .
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
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