Quenched path limits and periodization stability for tilted Brownian motion in Poissonian potentials on ${\mathbb{H}}^d$

Miklos Abert, Adam Arras, Jaelin Kim

We analyze the existence of Brownian motion tilted by a potential of full support on hyperbolic spaces ${\mathbb{H}}^d$. On compact spaces, it is classical that these path limits, ca…