000 02641nam a22003738i 4500
001 CR9781139872003
003 UkCbUP
005 20200124160215.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 140124s2015||||enk o ||1 0|eng|d
020 _a9781139872003 (ebook)
020 _z9781107075832 (hardback)
020 _z9781107428829 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA164
_b.R66 2015
082 0 0 _a511/.6
_223
100 1 _aRomik, Dan,
_d1976-
_eauthor.
245 1 4 _aThe surprising mathematics of longest increasing subsequences /
_cDan Romik.
264 1 _aCambridge :
_bCambridge University Press,
_c2015.
300 _a1 online resource (xi, 353 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aInstitute of Mathematical Statistics textbooks ;
_v4
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _a0. A few things you need to know -- 1. Longest increasing subsequences in random permutations -- 2. The Baik-Deift-Johansson theorem -- 3. Erdîos-Szekeres permutations and square Young tableaux -- 4. The corner growth process: limit shapes -- 5. The corner growth process: distributional results -- Appendix: Kingman's subadditive ergodic theorem.
520 _aIn a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.
650 0 _aCombinatorial analysis.
650 0 _aProbabilities.
776 0 8 _iPrint version:
_z9781107075832
830 0 _aInstitute of Mathematical Statistics textbooks ;
_v4.
856 4 0 _uhttps://doi.org/10.1017/CBO9781139872003
999 _c516177
_d516175