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We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
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2002
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2003
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1999
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J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the second row of a Young diagram under Plancherel measure
2000
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A. Borodin and G. Olshanski, Distributions on partitions, point processes and the hypergeometric kernel
2000
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A. Borodin, A. Okounkov and G. Olshanski, Asymptotics of Plancherel measures for symmetric groups
2000
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A. Borodin and A. Okounkov, A Fredholm determinant formula for Toeplitz determinants
2000
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P. Deift, Integrable systems and combinatorial theory
2000
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S. V. Kerov, Anisotropic Young diagrams and Jack symmetric functions
2000
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2003
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J. Fulman, Stein’s method, Jack measure, and the Metropolis algorithm
2004
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S. Kerov, G. Olshanski, and A. Vershik, Harmonic analysis on the infinite symmetric group
2004
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C. A. Tracy and H. Widom, A limit theorem for shifted Schur measures
2004
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A. Borodin and G. Olshanski, Harmonic analysis on the infinite–dimensional unitary group and determinantal point processes
2005
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A. Borodin and G. Olshanski, Z-measures on partitions and their scaling limits
2005
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A. Borodin and G. Olshanski, Random partitions and the Gamma kernel
2005
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W. König, Orthogonal polynomial ensembles in probability theory
2005
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Sho Matsumoto, Correlation functions of the shifted Schur measure
2005
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A. Okounkov, The uses of random partitions
2005
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A. Borodin and G. Olshanski, Meixner polynomials and random partitions
2006
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K. Johansson, Random matrices and determinantal processes
2006
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A. Okounkov, Random partitions
2006
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2007
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R. P. Stanley, Increasing and decreasing subsequences and their variants
2007
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G. Olshanski, Difference operators and determinantal point processes
2008
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P. J. Forrester, Log-gases and random matrices
2010
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2010
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L. Petrov, Random strict partitions and determinantal point processes
2010
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2010
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L. V. Bogachev and Z. Su, Gaussian fluctuations of Young diagrams under the Plancherel measure
2080
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