Eden Model in Many Dimensions

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Abstract
The Eden model in many dimensions is studied by an exact enumeration method. Our result including the first-order 1d correction has the asymptotic behavior 〈Rn2〉∼2 ln(n)(1+32d), which does not agree with the naive expectation R∼n1d [or d(n1d−1)]. This suggests that when n is large, 〈Rn2〉 might be a singular function of d. We also present a result on the Cayley tree.