000			02813nam a22003498i 4500
001			CR9781139107129
003			UkCbUP
005			20200124160234.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			110706s2009||||enk o ||1 0|eng|d
020			_a9781139107129 (ebook)
020			_z9780521133128 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA188 _b.B568 2009
082	0	4	_a512.9434 _222
100	1		_aBlower, G. _q(Gordon), _eauthor.
245	1	0	_aRandom matrices : _bhigh dimensional phenomena / _cGordon Blower.
264		1	_aCambridge : _bCambridge University Press, _c2009.
300			_a1 online resource (x, 437 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v367
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	2		_aMetric measure spaces -- Lie groups and matrix ensembles -- Entropy and concentration of measure -- Free entropy and equilibrium -- Convergence to equilibrium -- Gradient flows and functional inequalities -- Young tableaux -- Random point fields and random matrices -- Integrable operators and differential equations -- Fluctuations and the Tracy-Widom distribution -- Limit groups and Gaussian measures -- Hermite polynomials -- From the Ornstein-Uhlenbeck process to the Burgers equation -- Noncommutative probability spaces.
520			_aThis book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
650		0	_aRandom matrices.
776	0	8	_iPrint version: _z9780521133128
830		0	_aLondon Mathematical Society lecture note series ; _v367.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139107129
999			_c517948 _d517946