Asymptotic behavior of random heaps | Zendy

Hough J. B. | Zendy

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Asymptotic behavior of random heaps

Author(s) -

Hough J. B.

Publication year - 2005

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.20077

Subject(s) - heap (data structure) , mathematics , conjecture , struct , random walk , combinatorics , limit (mathematics) , boundary (topology) , discrete mathematics , mathematical analysis , statistics , computer science , algorithm , programming language

We consider a random walk W n on the locally free group (or equivalently a signed random heap) with m generators subject to periodic boundary conditions. Let #T ( W n ) denote the number of removable elements, which determines the heap's growth rate. We prove that lim n →∞ ( #T ( W n ))/ m ≤ 0.32893 for m ≥ 4. This result disproves a conjecture (due to Vershik, Nechaev and Bikbov [Comm Math Phys 212 (2000), 469–501]) that the limit tends to 1/3 as m → ∞. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005

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