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We study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the Mallows measure.
On representations of the symmetric group
G. de B. Robinson · 1938
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Non-null ranking models I
C. L. Mallows · 1957
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Longest increasing and decreasing subsequences
C. Schensted · 1961
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An introduction to probability theory and its applications. Vol. I
W. Feller · 1968
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Permutations, matrices and generalized Young tableaux
D.E. Knuth · 1970
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A few seedlings of research
J.M. Hammersley · 1972
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The theory of partitions
G. E. Andrews · 1976
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A variational problem for random Young tableaux
B.F. Logan and L.A. Shepp · 1977
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Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux
A.M. Vershik and S.V. Kerov · 1977
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The Representation Theory of the Symmetric Groups
G.D. James · 1978
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Group representations in probability and statistics
P. Diaconis · 1988
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Limiting curves for i.i.d. records
J.-D. Deuschel and O. Zeitouni · 1995
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Enumerative Combinatorics
R. Stanley · 1997
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Longest increasing subsequences:from patience sorting to the Baik-Deift-Johansson theorem
D.J. Aldous and P. Diaconis · 1999
Cited alongside, same era.
On the distribution of the length of the longest increasing subsequence of random permutations
J. Baik, P. Deift, and K. Johansson · 1999
Cited alongside, same era.
On increasing subsequences of i.i.d. samples
J.-D. Deuschel and O. Zeitouni · 1999
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Enumerative Combinatorics, Vol. 2
R. Stanley · 1999
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A universality property for last-passage percolation paths close to the axis
T. Bodineau and J. Martin · 2005
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A remark on a theorem of Chatterjee and last passage percolation
T. Suidan · 2006
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The probabilistic method
N. Alon and J. H. Spencer · 2008
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Sorting from noisy information
M. Braverman and E. Mossel · 2009
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Thermodynamic limit for the mallows model on S n S_{n}
S. Starr · 2009
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q q -exchangeability via quasi-invariance
A. Gnedin and G. Olshanski · 2010
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Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques
P. Diaconis and A. Ram · 2000
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Symmetrized random permutations
J. Baik and E.M. Rains · 2001
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A course in combinatorics, 2nd edition
J.H. van Lint and R.M. Wilson · 2001
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G L ( n , q ) GL(n,q) and increasing subsequences in nonuniform random permutations
J. Fulman · 2002
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A GUE central limit theorem and universality of directed first and last passage site percolation
J. Baik and T.M. Suidan · 2005
Cited alongside, same era.
The length of the longest increasing subsequence of a random Mallows permutation
C. Mueller and S. Starr · 2011
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Asymptotics of q q -Plancherel measures
V. Féray and P-L Méliot · 2012
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The two-sided infinite extension of the Mallows model for random permutations
A. Gnedin and G. Olshanski · 2012
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Central limit theorem for first-passage percolation time across thin cylinders
S. Chaterjee and P.S. Dey · 2013
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