Two observations on the capacity of the range of simple random walks on ℤ³ and ℤ⁴

2016/11/26 by Chang, Yinshan
#60J10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1611.08654

Abstract

We prove a weak law of large numbers for the capacity of the range of simple random walks on ℤ⁴. On ℤ³, we show that the capacity, properly scaled, converges in distribution towards the corresponding quantity for three dimensional Brownian motion.

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