Resumen de Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models
Let Bs be a d-dimensional Brownian motion and ω(dx) be an independent Poisson field on Rd. The almost sure asymptotics for the logarithmic moment generating function logE0exp{±θ∫t0V¯¯¯¯(Bs)ds}(t→∞) are investigated in connection with the renormalized Poisson potential of the form V¯¯¯¯(x)=∫Rd1|y−x|p[ω(dy)−dy],x∈Rd.
The investigation is motivated by some practical problems arising from the models of Brownian motion in random media and from the parabolic Anderson models.
