Heat kernel on affine buildings

Monday, December 8, 2014 -
3:15pm to 4:30pm
Let $\mathscr{X}$ be a thick affine building of rank $r+1$. We consider a finite range isotropic random walk on vertices of $\mathscr{X}$. Our main focus is to obtain the optimal global upper and lower bounds for the $n$'th iteration of the transition operator uniform in the region $\text{dist}\big(n^{-1} \delta(O, x), \partial \mathcal{M}\big) \geq Kn^{-1/\eta}$ where $\delta$ is the generalized distance and $\mathcal{M}$ is the convex hull of $\big\{\delta(O, x) : p(O, x) > 0\big\}$. 
Bartosz Trojan
Uniwersytet Wroclawski, Poland
Event Location: 
Fine Hall 314