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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 4(340), Pages 97–128 (Mi umn417)  

This article is cited in 9 scientific papers (total in 9 papers)

The Wulff construction in statistical mechanics and combinatorics

S. B. Shlosmanab

a CNRS – Center of Theoretical Physics
b Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: Geometric solutions are presented for some variational problems of statistical mechanics and combinatorics, and the Wulff construction predicting crystal shapes is discussed along with a construction determining the shape of a typical Young diagram and a typical skyscraper.

DOI: https://doi.org/10.4213/rm417

Full text: PDF file (446 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2001, 56:4, 709–738

Bibliographic databases:

UDC: 531.19
MSC: Primary 49Q20, 82D25; Secondary 82B44, 74N05, 74N20
Received: 26.01.2001

Citation: S. B. Shlosman, “The Wulff construction in statistical mechanics and combinatorics”, Uspekhi Mat. Nauk, 56:4(340) (2001), 97–128; Russian Math. Surveys, 56:4 (2001), 709–738

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Journal of Mathematical Sciences (New York), 126:2 (2005), 1128–1132  mathnet  crossref  mathscinet  zmath
    2. Funaki T., “Stochastic interface models”, Lectures on probability theory and statistics, Lecture Notes in Math., 1869, Springer, Berlin, 2005, 103–274  crossref  mathscinet  isi
    3. Bodineau T., Schonmann R.H., Shlosman S., “3D crystal: how flat its flat facets are?”, Comm. Math. Phys., 255:3 (2005), 747–766  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. Erlihson M.M., Granovsky B.L., “Limit shapes of Gibbs distributions on the set of integer partitions: the expansive case”, Ann. Inst. Henri Poincaré Probab. Stat., 44:5 (2008), 915–945  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Borodin A., Shlosman S., “Gibbs ensembles of nonintersecting paths”, Comm. Math. Phys., 293:1 (2010), 145–170  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Tadahisa Funaki, Makiko Sasada, “Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams”, Comm Math Phys, 2010  crossref  mathscinet  isi  scopus  scopus
    7. Dai Liang Ma, Hsuen Li Chen, “Use of simple thermal annealing processes to prepare free-standing platinum rods”, CrystEngCommun, 12:10 (2010), 2896  crossref  isi  scopus  scopus
    8. Okounkov A., “Limit shapes, real and imagined”, Bull. Amer. Math. Soc., 53:2 (2016), 187–216  crossref  mathscinet  zmath  isi  elib  scopus
    9. O. V. Ogievetskii, S. B. Shlosman, “Plane Partitions and Their Pedestal Polynomials”, Math. Notes, 103:5 (2018), 793–796  mathnet  crossref  crossref  isi  elib
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