Random random walks on the integers mod n

A note on inverse results of random walks in Abelian groups

“…We also refer the reader to several results by Hildebrand and coauthors in [4,10,3] for similar statements with non-symmetric random walks in Z/qZ. More concretely, [4, Theorem 1] says that the m-step random walk over {a 1 , .…”

“…Now we give our result for this model, stated in the symmetric setting. 3 Theorem 1.15 (Inverse result for ρ m in torsion-free setting). Let ε < 1 and C be positive constants.…”

A survey of results on random random walks on finite groups

“…Proof of Lemma 5: Although Dai and Hildebrand [2] used a different method, the proof of this lemma can proceed in a manner similar to the proof of Theorem 6 for k ≥ 3; however, one must be careful in proving the analogue of Lemma 2. Note in particular that instead of ranging over −(n − 1)/2, .…”

“…For some constant γ > 0 and m = ⌊γn 2/(k−1) ⌋, Dai and Hildebrand [2] generalized the result of Theorem 6 to the case where n need not be prime. One needs to be cautious in determining which values to pick for a 1 , .…”

“…We shall consider 3 categories of values for j. The proofs for the first and third categories use ideas from [2]. The proof for the second category at times diverges from the proof in [2]; the ideas in this alternate presentation were discussed in personal communications between the authors of [2].…”