Large deviations and renormalization for Riesz potentials of stable intersection measures
- Chen, Xia
- Rosen, Jay
DOIAbstract
AbstractWe study the object formally defined as (0.1)γ([0,t]2)=∬[0,t]2|Xs−Xr|−σdrds−E∬[0,t]2|Xs−Xr|−σdrds, where Xt denotes the symmetric stable processes of index 0<β≤2 in Rd. When β≤σ<min{32β,d}, this has to be defined as a limit, in the spirit of renormalized self-intersection local time. We obtain results about the large deviations and laws of the iterated logarithm for γ. This is applied to obtain results about stable processes in random potentials
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