The square of self intersection local time of Brownian motion (Q2702436)

Let \(L_\varepsilon(t)\) be the regularization of the self intersection of a \(d\)-dimensional Brownian motion, defined by NEWLINE\[NEWLINEL_\varepsilon(t)= \int^t_0 dt_2\int^{t_2}_0 dt_1(2\pi\varepsilon)^{- d/2} e^{-|B(t_2)- B(t_1)|^2}.NEWLINE\]NEWLINE The authors proved [``The renormalization of self intersection local times. I: The chaos expansion'' (to appear in Inf. Dimensional Anal. Q. Probab.)] that, multiplied by some renormalization factor \(r(\varepsilon, d)\), every term in the chaos expansion of \(L_\varepsilon(t)\) converges in law, as \(\varepsilon\to 0\), to a Brownian motion. In this paper, they compute explicitly, for \(d\geq 4\), the limit in law of the variance of \(r(\varepsilon, d)L_\varepsilon(t)\).NEWLINENEWLINEFor the entire collection see [Zbl 0953.00048].