Abstract
For any finitely generated group G, let n ---> Φ_G(n) be the function that describes the rough asymptotic behavior of the probability of return to the identity element at time 2n of a symmetric simple random walk on G (this is an invariant of quasi-isometry). We determine this function when G is the free solvable group S_{d,r} of derived length d on r generators and some other related groups.
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