5 problems

Nonexistence conjecture. For $\beta<1$, the renormalized SILT $\tilde{\gamma}_X$ does not exist when

Let $W$ be the Brownian motion and let $G$ be the Green kernel appearing in the definition of the renormalised Amperean area. Write $I_W$ for the recentred self-intersection local…

Let $B$ be a $d$-dimensional Brownian motion, let $k=(k_1,\ldots,k_d)$ be a multiindex with $|k|=k_1+\cdots+k_d$, and define … where $p_{d,\epsilon}$ is the $d$-dimensional Gaussia…

Let $\widehat{\alpha}^{'}_{t,\varepsilon}(0)$ denote the regularized first-order derivative of the self-intersection local time at zero for one-dimensional fractional Brownian moti…

Let $I$ be the rate function for the normalized self-intersection local time, and let $\lambda_d$ be the corresponding typical value in dimensions $d\geq 3$. Self-intersection rate…