2 problems

For two independent planar Brownian motions $X$ and $X'$, let $\theta_X(z)$ and $\theta_{X'}(z)$ denote their winding numbers around $z$, and define … Let $\ell$ be the intersectio…

Let $B$ be the bounded domain and let $I$ be the rate function whose variational representation is … In the case $b=(1,\dots,1)$, a minimising tuple $(\psi_1,\dots,\psi_p)$ in this…