Large deviations and renormalization for Riesz potentials of stable intersection measures

We study the object formally defined as equation(0.1)γ([0,t]2)=∬[0,t]2|Xs−Xr|−σdrds−E∬[0,t]2|Xs−Xr|−σdrds, where XtXt denotes the symmetric stable processes of index 0<β≤20<β≤2 in RdRd. When β≤σ