LEADER 03858nam 2200637 a 450 001 9910438137603321 005 20200520144314.0 010 $a1-283-90946-4 010 $a1-4614-6025-5 024 7 $a10.1007/978-1-4614-6025-1 035 $a(CKB)2670000000278609 035 $a(EBL)1082062 035 $a(OCoLC)820204654 035 $a(SSID)ssj0000799143 035 $a(PQKBManifestationID)11497635 035 $a(PQKBTitleCode)TC0000799143 035 $a(PQKBWorkID)10762929 035 $a(PQKB)10887864 035 $a(DE-He213)978-1-4614-6025-1 035 $a(MiAaPQ)EBC1082062 035 $a(PPN)16830452X 035 $a(EXLCZ)992670000000278609 100 $a20121022e20131996 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe self-avoiding walk /$fNeal Madras, Gordon Slade 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (435 p.) 225 0$aModern Birkhauser classics 300 $aReprint of the 1996 edition. 300 $a"Originally published in the series Probability and its applications"--T.p. verso. 311 $a1-4614-6024-7 320 $aIncludes bibliographical references and index. 327 $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. . 330 $aThe self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition?a path on a lattice that does not visit the same site more than once?it is difficult to analyze mathematically. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics and in chemistry, and to give an introduction to some of the nonrigorous methods used in those fields.    Topics covered in the book include: the lace expansion and its application to the self-avoiding walk in more than four dimensions where most issues are now resolved; an introduction to the nonrigorous scaling theory; classical work of Hammersley and others; a new exposition of Kesten?s pattern theorem and its consequences; a discussion of the decay of the two-point function and its relation to probabilistic renewal theory; analysis of Monte Carlo methods that have been used to study the self-avoiding walk; the role of the self-avoiding walk in physical and chemical applications. Methods from combinatorics, probability theory, analysis, and mathematical physics play important roles. The book is highly accessible to both professionals and graduate students in mathematics, physics, and chemistry.  . 410 0$aModern Birkhäuser Classics,$x2197-1803 606 $aSelf-avoiding walks (Mathematics) 606 $aStatistical physics 606 $aChemistry, Physical and theoretical$xMathematics 615 0$aSelf-avoiding walks (Mathematics) 615 0$aStatistical physics. 615 0$aChemistry, Physical and theoretical$xMathematics. 676 $a519.233 700 $aMadras$b Neal$065909 701 $aSlade$b G$g(Gordon)$0296628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438137603321 996 $aThe self-avoiding walk$94202897 997 $aUNINA LEADER 01130nam0-2200349 --450 001 9910834700903321 005 20250729124457.0 010 $a978-0-19-888853-6$bpack 010 $a978-0-19-287122-0$bvol. 1 010 $a978-0-19-287123-7$bvol. 2 100 $a20240306d2023----kmuy0itay5050 ba 101 2 $aeng$alat$agrc 102 $aGB 105 $a 001yy 200 1 $a<>Fragments and Periochae$fLivy$gedited with an introduction, translation, and commentary by D. S. Levene 210 $aOxford$cOxford University Press$d2023 215 $av.$d25 cm 327 0 $a1.: Fragments, citations, testimonia$a2.: Periochae 1-45 676 $a937.04$v23$zita 676 $a878$v23$zita 700 1$aLivius,$bTitus$f<59 a. C.-17>$05194 702 1$aLevene,$bD.S. 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910834700903321 952 $aP2B 650 LIVIUS T 403 (1) 2023$b2024/645$fFLFBC 952 $aIV ZR 240 (1)$b2025/1049$fFGBC 952 $aIV ZR 240 (2)$b2025/1049$fFGBC 959 $aFLFBC 959 $aFGBC 996 $aFragments and Periochae$94410142 997 $aUNINA