Invariance Principle for a Random Walk Among a Poisson Field of Moving Traps

Abstract: We consider a random walk along a Poisson cloud of moving traps on Z ^ d, where the walk is killed at a rate professional to the number of traps capturing the same position In dimension d=1, we have previously shown that under the anneled law of the random walk conditioned on survival up to time t, the walk is sub diffuse Here we show that in d>=6, this anneled law satisfies an variance principle under differential scaling Our proof is based on the theory of thermodynamic formalism, where we extend some classic results for Markov shifts with a potential of summary variation and a final alpha to the case of an uncountable non compact alpha Based on joint work with Siva Athreya and Alexander Drewitz.