For d ≥ 5 the random walk on a Poissonian field of independent random walks satisfies a strong law and large deviation bounds, and for d ≥ 9 an annealed functional central limit theorem is claimed, for every positive particle density.
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Random walks on random walks: non-perturbative results in high dimensions
For d ≥ 5 the random walk on a Poissonian field of independent random walks satisfies a strong law and large deviation bounds, and for d ≥ 9 an annealed functional central limit theorem is claimed, for every positive particle density.