Abstract:
We present a techniques for obtaining the limit shapes of Yong diagrams with respect to multiplicative measures, which arise in statistical mechanics. Our approach does not use neither complex analysis, nor Tauberian theorems. Also, we get the limit shape for bounded and unbounded partitions with respect to uniform measure, avoiding even generating functions. Bibl. – 6 titles.
Citation:
F. Petrov, “Limits shapes of Young diagrams. Two elementary approaches”, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Zap. Nauchn. Sem. POMI, 370, POMI, St. Petersburg, 2009, 111–131; J. Math. Sci. (N. Y.), 166:1 (2010), 63–74
\Bibitem{Pet09}
\by F.~Petrov
\paper Limits shapes of Young diagrams. Two elementary approaches
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~40
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 370
\pages 111--131
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3534}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 166
\issue 1
\pages 63--74
\crossref{https://doi.org/10.1007/s10958-010-9845-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77949294422}
Linking options:
https://www.mathnet.ru/eng/znsl3534
https://www.mathnet.ru/eng/znsl/v370/p111
This publication is cited in the following 5 articles:
Walter Bridges, “Limit shapes for unimodal sequences”, Int. J. Number Theory, 19:05 (2023), 1111
Dalal A.J., Lohss A., Parry D., “Statistical Structure of Concave Compositions”, Ann. Comb., 25:3 (2021), 729–756
Melczer S., Panova G., Pemantle R., “Counting Partitions Inside a Rectangle”, SIAM Discret. Math., 34:4 (2020), 2388–2410
Tadahisa Funaki, “Equivalence of Ensembles Under Inhomogeneous Conditioning and Its Applications to Random Young Diagrams”, J Stat Phys, 154:1-2 (2014), 588
Dan Beltoft, Cédric Boutillier, Nathanaël Enriquez, “Random Young Diagrams in a Rectangular Box”, Mosc. Math. J., 12:4 (2012), 719–745
Citation in format AMSBIB
Contact us: