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An Invariance Principle for a Random Walk Among Moving Traps

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SSDW01 - Self-interacting processes

We consider a random walk among a Poisson cloud of moving traps on Z^d, where the walk is killed at a rate proportional to the number of traps occupying the same position. In dimension d=1, it was previously shown that under the annealed law of the random walk conditioned on survival up to time t,the walk is sub-diffusive. We show that in d>=6 and under diffusive scaling, this annealed law satisfies an invariance principle with a positive diffusion constant if the killing rate is small. Our proof is based on the theory of thermodynamic formalism, where we extend some classic results for Markov shifts with a finite alphabet and a potential of summable variation to the case of an uncountable non-compact alphabet. Based on joint work with S. Athreya and A. Drewitz.

This talk is part of the Isaac Newton Institute Seminar Series series.

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