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Mosc. Math. J., 2006, Volume 6, Number 3, Pages 553–566 (Mi mmj260)  

This article is cited in 38 scientific papers (total in 38 papers)

The birth of a random matrix

A. Yu. Okounkova, N. Yu. Reshetikhinb

a Princeton University
b University of California, Berkeley

Abstract: We consider the behavior of a random stepped surface near a turning point, that is, a point at which the limit shape is not smooth. When the turning point is a smooth point of the frozen boundary, the resulting point process is identified with the standard Gaussian measure on infinite Hermitian matrices. A different point process appears if the turning point is a cusp of the frozen boundary.

Key words and phrases: Random matrices, random surfaces.

DOI: https://doi.org/10.17323/1609-4514-2006-6-3-553-566

Full text: http://www.ams.org/.../abst6-3-2006.html
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Bibliographic databases:

MSC: 15A52, 60G60
Received: June 4, 2006
Language:

Citation: A. Yu. Okounkov, N. Yu. Reshetikhin, “The birth of a random matrix”, Mosc. Math. J., 6:3 (2006), 553–566

Citation in format AMSBIB
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\paper The birth of a~random matrix
\jour Mosc. Math.~J.
\yr 2006
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\issue 3
\pages 553--566
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    Citing articles on Google Scholar: Russian citations, English citations
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    6. Borodin A., Duits M., “Limits of determinantal processes near a tacnode”, Ann. Inst. Henri Poincaré Probab. Stat., 47:1 (2011), 243–258  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    14. Metcalfe A.P., “Universality Properties of Gelfand-Tsetlin Patterns”, Probab. Theory Relat. Field, 155:1-2 (2013), 303–346  crossref  mathscinet  zmath  isi  elib  scopus
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    17. Petrov L., “Asymptotics of Random Lozenge Tilings Via Gelfand-Tsetlin Schemes”, Probab. Theory Relat. Field, 160:3-4 (2014), 429–487  crossref  mathscinet  zmath  isi  elib  scopus
    18. Gorin V., “From Alternating Sign Matrices To the Gaussian Unitary Ensemble”, Commun. Math. Phys., 332:1 (2014), 437–447  crossref  mathscinet  zmath  isi  scopus
    19. Mkrtchyan S., “Plane Partitions With Two-Periodic Weights”, Lett. Math. Phys., 104:9 (2014), 1053–1078  crossref  mathscinet  zmath  isi  elib  scopus
    20. Adler M. Nordenstam E. Van Moerbeke P., “the Dyson Brownian Minor Process”, Ann. Inst. Fourier, 64:3 (2014), 971–1009  crossref  mathscinet  zmath  isi
    21. Gorin V., Shkolnikov M., “Multilevel Dyson Brownian Motions Via Jack Polynomials”, Probab. Theory Relat. Field, 163:3-4 (2015), 413–463  crossref  mathscinet  zmath  isi  elib  scopus
    22. Gorin V. Panova G., “Asymptotics of Symmetric Polynomials With Applications To Statistical Mechanics and Representation Theory”, Ann. Probab., 43:6 (2015), 3052–3132  crossref  mathscinet  zmath  isi  elib  scopus
    23. Panova G., “Lozenge Tilings With Free Boundaries”, Lett. Math. Phys., 105:11 (2015), 1551–1586  crossref  mathscinet  zmath  isi  scopus
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    25. Borodin A. Gorin V., “General -Jacobi Corners Process and the Gaussian Free Field”, Commun. Pure Appl. Math., 68:10 (2015), 1774–1844  crossref  mathscinet  zmath  isi  elib  scopus
    26. Garin V., Shkolnikov M., “Limits of Multilevel Tasep and Similar Processes”, Ann. Inst. Henri Poincare-Probab. Stat., 51:1 (2015), 18–27  crossref  mathscinet  isi  scopus
    27. Adler M., van Moerbeke P., “Coupled Gue-Minor Processes and Domino Tilings”, Int. Math. Res. Notices, 2015, no. 21, 10987–11044  crossref  mathscinet  zmath  isi  elib  scopus
    28. Sodin S., “a Limit Theorem At the Spectral Edge For Corners of Time-Dependent Wigner Matrices”, Int. Math. Res. Notices, 2015, no. 17, 7575–7607  crossref  mathscinet  zmath  isi  elib  scopus
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    30. Jeong I.-J. Sodin S., “a Limit Theorem For Stochastically Decaying Partitions At the Edge”, Random Matrices-Theor. Appl., 5:4 (2016), 1650016  crossref  mathscinet  zmath  isi
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