LEADER 03581nam 22006492 450 001 9910457872203321 005 20151005020621.0 010 $a1-107-14767-0 010 $a1-282-39477-0 010 $a9786612394775 010 $a0-511-64435-3 010 $a0-511-64813-8 010 $a0-511-18750-5 010 $a0-511-56649-2 010 $a0-511-61091-2 010 $a0-511-18657-6 035 $a(CKB)1000000000353322 035 $a(EBL)256691 035 $a(OCoLC)569384451 035 $a(SSID)ssj0000279005 035 $a(PQKBManifestationID)11222258 035 $a(PQKBTitleCode)TC0000279005 035 $a(PQKBWorkID)10258337 035 $a(PQKB)10094866 035 $a(UkCbUP)CR9780511610912 035 $a(MiAaPQ)EBC256691 035 $a(Au-PeEL)EBL256691 035 $a(CaPaEBR)ebr10124710 035 $a(CaONFJC)MIL239477 035 $a(EXLCZ)991000000000353322 100 $a20090910d2004|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElements of the random walk $ean introduction for advanced students and researchers /$fJoseph Rudnick, George Gaspari$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2004. 215 $a1 online resource (xv, 329 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-53583-2 311 $a0-521-82891-0 320 $aIncludes bibliographical references (p. 323-325) and index. 327 $aCover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Introduction to techniques; 2 Generating functions I; 3 Generating functions II: recurrence, sites visited, and the role of dimensionality; 4 Boundary conditions, steady state, and the electrostatic analogy; 5 Variations on the random walk; 6 The shape of a random walk; 7 Path integrals and self-avoidance; 8 Properties of the random walk: introduction to scaling; 9 Scaling of walks and critical phenomena; 10 Walks and the O(n) model: mean field theory and spin waves; 11 Scaling, fractals, and renormalization 327 $a12 More on the renormalization groupReferences; Index 330 $aRandom walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers. 606 $aRandom walks (Mathematics) 615 0$aRandom walks (Mathematics) 676 $a519.2/82 700 $aRudnick$b Joseph Alan$f1944-$0293348 702 $aGaspari$b George David 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910457872203321 996 $aElements of the random walk$92442231 997 $aUNINA