Bogachev, LV (2014) Limit shape of random convex polygonal lines: even more universality. Journal of Combinatorial Theory, Series A, 127. pp. 353-399. ISSN 0097-3165
Abstract
The paper concerns the limit shape (under some probability measure) of convex polygonal lines with vertices on Z+2, starting at the origin and with the right endpoint n=(n1,n2)→∞. In the case of the uniform measure, an explicit limit shape γ⁎:={(x1,x2)∈R+2:1−x1+x2=1} was found independently by Vershik (1994) [19], Bárány (1995) [3], and Sinaĭ (1994) [16]. Recently, Bogachev and Zarbaliev (1999) [5] proved that the limit shape γ⁎ is universal for a certain parametric family of multiplicative probability measures generalizing the uniform distribution. In the present work, the universality result is extended to a much wider class of multiplicative measures, including (but not limited to) analogs of the three meta-types of decomposable combinatorial structures — multisets, selections, and assemblies. This result is in sharp contrast with the one-dimensional case where the limit shape of Young diagrams associated with integer partitions heavily depends on the distributional type.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2014, Elsevier. This is an author produced version of a paper published in Journal of Combinatorial Theory, Series A. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Convex lattice polygonal line; Limit shape; Multiplicative measures; Local limit theorem; Möbius inversion formula; Generating function; Cumulants |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Mar 2015 10:35 |
Last Modified: | 10 May 2019 14:47 |
Published Version: | http://dx.doi.org/10.1016/j.jcta.2014.07.005 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jcta.2014.07.005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83405 |