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CATEGORIES:Probability
SUMMARY:Lengths of Monotone Subsequences in a Mallows Perm
utation - Nayantara Bhatnagar (University of Delaw
are)
DTSTART;TZID=Europe/London:20140121T163000
DTEND;TZID=Europe/London:20140121T173000
UID:TALK49248AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49248
DESCRIPTION:The longest increasing subsequence (LIS) of a unif
ormly random permutation\nis a well studied proble
m. Vershik-Kerov and Logan-Shepp first showed that
\nasymptotically the typical length of the LIS is
2sqrt(n). This line of\nresearch culminated in the
work of Baik-Deift-Johansson who related this\nle
ngth to the Tracy-Widom distribution.\n\nWe study
the length of the LIS and LDS of random permutatio
ns drawn from\nthe Mallows measure\, introduced by
Mallows in connection with ranking\nproblems in s
tatistics. Under this measure\, the probability of
a\npermutation p in S_n is proportional to q^Inv(
p) where q is a real\nparameter and Inv(p) is the
number of inversions in p. We determine the\ntypic
al order of magnitude of the LIS and LDS\, large d
eviation bounds for\nthese lengths and a law of la
rge numbers for the LIS for various regimes of\nth
e parameter q.\n\nThis is joint work with Ron Pele
d.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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