000			03596nam a22005175i 4500
001			978-1-4614-6025-1
003			DE-He213
005			20140220082823.0
007			cr nn 008mamaa
008			121116s2013 xxu| s |||| 0|eng d
020			_a9781461460251 _9978-1-4614-6025-1
024	7		_a10.1007/978-1-4614-6025-1 _2doi
050		4	_aQA273.A1-274.9
050		4	_aQA274-274.9
072		7	_aPBT _2bicssc
072		7	_aPBWL _2bicssc
072		7	_aMAT029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aMadras, Neal. _eauthor.
245	1	4	_aThe Self-Avoiding Walk _h[electronic resource] / _cby Neal Madras, Gordon Slade.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Birkhäuser, _c2013.
300			_aXVI, 427 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aPreface.-  Introduction -- Scaling, polymers and spins -- Some combinatorial bounds -- Decay of the two-point function -- The lace expansion -- Above four dimensions -- Pattern theorems -- Polygons, slabs, bridges and knots -- Analysis of Monte Carlo methods -- Related Topics -- Random walk -- Proof of the renewal theorem -- Tables of exact enumerations -- Bibliography -- Notation -- Index. .
520			_aThe self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition—a path on a lattice that does not visit the same site more than once—it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields.    Topics covered in the book include: the lace expansion and its application to the self-avoiding walk in more than four dimensions where most issues are now resolved; an introduction to the nonrigorous scaling theory; classical work of Hammersley and others; a new exposition of Kesten’s pattern theorem and its consequences; a discussion of the decay of the two-point function and its relation to probabilistic renewal theory; analysis of Monte Carlo methods that have been used to study the self-avoiding walk; the role of the self-avoiding walk in physical and chemical applications. Methods from combinatorics, probability theory, analysis, and mathematical physics play important roles. The book is highly accessible to both professionals and graduate students in mathematics, physics, and chemistry.
650		0	_aMathematics.
650		0	_aCombinatorics.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aCombinatorics.
650	2	4	_aMathematical Applications in the Physical Sciences.
650	2	4	_aMathematical Physics.
700	1		_aSlade, Gordon. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461460244
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-6025-1
912			_aZDB-2-SMA
999			_c95566 _d95566