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SUMMARY:Lengths of Monotone Subsequences in a Mallows Permutation - Nayant
 ara Bhatnagar (University of Delaware)
DTSTART:20140121T163000Z
DTEND:20140121T173000Z
UID:TALK49248@talks.cam.ac.uk
CONTACT:24873
DESCRIPTION:The longest increasing subsequence (LIS) of a uniformly random
  permutation\nis a well studied problem. Vershik-Kerov and Logan-Shepp fir
 st 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\nlength to the Tracy-Widom distribution.\n\nWe study the leng
 th of the LIS and LDS of random permutations drawn from\nthe Mallows measu
 re\, introduced by Mallows in connection with ranking\nproblems in statist
 ics. Under this measure\, the probability of a\npermutation p in S_n is pr
 oportional to q^Inv(p) where q is a real\nparameter and Inv(p) is the numb
 er of inversions in p. We determine the\ntypical order of magnitude of the
  LIS and LDS\, large deviation bounds for\nthese lengths and a law of larg
 e numbers for the LIS for various regimes of\nthe parameter q.\n\nThis is 
 joint work with Ron Peled.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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