ar X iv : m at h / 04 07 28 6 v 1 [ m at h . PR ] 1 6 Ju l 2 00 4 1 ASYMPTOTIC BEHAVIOR OF RANDOM HEAPS
نویسنده
چکیده
Let Wn be a random walk on the locally free group with m generators subject to periodic boundary conditions, and let T (Wn) be the set of removable elements. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik et. al. [3]) that the limit tends to 1 3 as m → ∞.
منابع مشابه
ar X iv : m at h / 04 07 28 6 v 2 [ m at h . PR ] 6 M ar 2 00 5 1 ASYMPTOTIC BEHAVIOR OF RANDOM HEAPS
We consider a random walk Wn on the locally free group (or equivalently a signed random heap) with m generators subject to periodic boundary conditions. Let #T (Wn) denote the number of removable elements, which determines the heap's growth rate. We prove that limn→∞ E(#T (Wn)) m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik, Nechaev and Bikbov [4]) that the limit tend...
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