The process of bone tissue repair and regeneration is complex and requires a variety of physiological signals, including biochemical, electrical and mechanical signals, which collaborate to ensure functional recovery. The...
We study the decay of convolution powers of a large family µS,a of measures on finitely generated nilpotent groups. Here, S = (s1, . . . , s k ) is a generating k-tuple of group elements and a = (α1, . . . , α k ) is a k-tuple of reals in the interval (0, 2). The symmetric measure µS,a is supported bym ∈ Z} and gives probability proportional to (1 + m) −α i −1 to s ±m i , i = 1, . . . , k, m ∈ N. We determine the behavior of the probability of return µ (n) S,a (e) as n tends to infinity. This behavior depends in somewhat subtle ways on interactions between the k-tuple a and the positions of the generators si within the lower central series Gj = [Gj−1, G], G1 = G.
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